Study of Conditional ML Estimators in Time and Frequency domain System Identification.

The Special Issue in Honor of Aman Ullah:AnOverview∗Esfandiar Maasoumi,and Qi Li1A Brief history of Aman Ullah and his seminal contributions to EconometricsFor about four decades,Aman Ullah has been a leading scholar in thefiled of econometrics.Several of his professional colleagues,friends and students decided to have a major special issue of a refereed journal to honor his many contributions to thefield.There was also a related conference in his honor at Chengdu,China in2012.This special issue is thus dedicated to Aman,the scholar,teacher and friend.Aman Ullah obtained his BA in Statistics,Economics,and Mathematics fol-lowed by an MS in Mathematical Statistics from Lucknow University in Uttar Pradesh India.He completed his Ph.D in Economics at the University of Delhi, India.He then relocated to North America where he has held posts at Southern Methodist University,the University of Western Ontario,and the University of California Riverside where he currently holds the post of Distinguished Univer-sity Professor.Aman has been an Associate Editor and Board member of Econometric Re-views since1987,having served as long as the editor.He has served and serves on numerous other editorial boards,such as Journal of Quantitative Economics, Journal of Nonparametric Statistics,Empirical Economics,Sankhya,and Amer-ican Journal of Mathematical and Management Sciences.He is the Series Editor for Statistics and Econometrics published by Chapman-Hall/Taylor-Francis.Aman has made seminal contributions in a number of sub-disciplines in Econometrics including nonparametric estimation and inference,finite-sample theory,information theory,and shrinkage methods.He has formidable list of publications that number well over100in the leading journals,including Econo-metrica,Journal of Econometrics,Journal of Business and Economic Statistics, Journal of the American Statistical Association,Review of Economic and Statis-tics,Econometric Theory and the Journal of Applied Econometrics.He has authored or co-authored eight books:1.Finite Sample Econometrics,2004(Oxford:Oxford University Press).∗Grateful thanks to Jeffrey Racine and Feng Yao for input and help with this over view.12.Handbook of Applied Econometrics and Statistical Inference,2002edited(New York:Marcel Dekker)(with A.Wan and A.Chaturvedi).3.Handbook of Applied Economic Statistics,edited,1998(New York:Mar-cel Dekker)(with D.E.A.Giles625).4.Contributions to Econometric Theory and Applications,1990,edited(NewYork:Springer-Verlag)(with Carter and Dutta).5.Nonparametric Econometrics,1999(New York:Cambridge UniversityPress)(with Pagan).6.Econometrics:A Varying Coefficients Approach,1981(England:CroomHelm)(with Raj).7.Recent Advances in Regression methods,November1981(New York:Mar-cel Dekker)(with Vinod).8.Semi Parametric and Nonparametric Econometrics,1988,edited for Em-pirical Economics,(Heidelberg:Physica-Verlag).As an educator Aman has mentored scores of Ph.D.students,serving as the main supervisor for K.Kadiyala,A.Hoque,L.Magee,F.Camacho,S.Power, T.Peters,P.Rilstone,J.Racine,Y.Fan,A.Ngereng,Z.Zhou,M.Tengesdal, M.Mercurio,S.Kumar,K.Mundra,G.Popli,D.Mukherjee,D.Henderson,Y. Bao,D.Chambers,M.Das,S.Dhongde,B.Gress,W.Sun,and X.Huang,and as a committee member on far too many dissertations to list here.Aman’s commitment as an educator,mentor,and his seemingly limitless fountain of inspiration is highlighted in the various contributions contained in this special issue in his honor.He is known for his modesty and spirituality. Combined with his unique and enduring scholarly creativity,he continues to be a great presence in our profession.As we pen this foreword,Aman,we would like to underscore the fact that you honor us with your virtual presence in your work,your physical presence during our studies and at conferences and workshops,and your spiritual presence where you humbly lead by example demonstrating the highest qualities that academics could strive for.The papers in this Special Issue can be placed into four categories:1.Endo-geneity;2.Nonparametric/semiparametric estimation methods;3.Hypothesis testing;4.Parametric methods in constructing common factors and estimating conditional variance.2Endogeneity.Thefirst category consists of six papers.Baltagi and Deng propose a3SLS estimator for a simultaneous system of spatial autoregressive equations with random effects,which can handle endoegeneity,spatial lag dependence,hetero-geneity and cross equation correlation.The Monte Carlo experiments suggest2there is potential gain infinite sample efficiency.Cai,Chen and Fang propose a three-stage estimation for a semiparametric dynamic panel data model,wherethe regressors may contain lagged dependent variables and endogenous vari-ables.Thefirst two stages involve estimating all coefficients with nonparametric GMM and estimating the parametric coefficient by an averaging method.Thethird stage produces an estimator of the varying coefficient from partial residu-als.They derive the consistency and asymptotic normality of both estimators. Monte Carlo simulations demonstrate that the proposed estimator performswell infinite sample settings.Hirano and Porter consider statistical models in which the mapping from the reduced form distribution to the structural param-eters is singular.This implies that the point estimators cannot be unbiased, quantile-unbiased,or translation equivalent.Bias reduction procedures cannotfully remove bias,and face a nontrivial bias-variance tradeoffinfinite samples. Escanciano and Zhu consider a two-step semiparametric estimator for the sam-ple selection model,where the bandwidth for the nonparametric component is chosen to minimize the mean squared error of thefitted semiparametric model.The paper demonstrates that the data-driven estimator is asymptotically normaland uniform in the bandwidth.A Monte Carlo study suggests that the estima-tor has excellentfinite sample performance.Dong,Gan and Wang propose anew model to identify if and how much the educational attainment gap between blacks and whites is due to the difference in their neighborhoods.There is a substantial neighborhood effect for the movers who belong to the endogenous type,who may move in response to the neighborhood effect on their education.The endogenous type has more education and moves more often than the exoge-nous type,who may move for reasons unrelated to education.On average,theyfind that the neighborhood variable(the percentage of high school graduatesin the neighborhood)accounts for about28.96%of the education gap between blacks and whites.Ai and Meng consider a semiparametric panel binary choice model withfixed effects and continuous endogenous regressors.Afirst stage nonparametric panel regression withfixed effect generates estimated residuals.The smoothed maximum score estimation is performed in the second stage to estimate the parameters with the residuals as an added regressor.They obtainthe consistency and asymptotic normality of thefinite dimensional parameterand illustrate solidfinite sample performance in a simulation study.3Nonparametric/semiparametric estimation meth-ods.There are six papers in this category.Fan and Liu propose a symmetrized multivariate k-NN estimator for the conditional mean and for the conditional distribution function,and provide the asymptotic properties.The asymptotic distribution of the proposed k-NN estimator does not depend on the existence ofthe marginal probability density function of the covariates.The simulation illus-trates improvement over the Nadaraya-Watson estimator at evaluation points3away from the center.Saart,Gao and Allen propose a semiparametric regres-sion approach to a nonlinear Autoregressive Conditional Duration model that allowsflexibilities in the dynamics of the conditional duration model and the shape of the hazard function.The estimation is performed via an iterative al-gorithm.They establish the semiparametric estimators’asymptotic properties and illustrate that the estimators exhibit robustfinite sample performance in simulations.Liang,Lin and Hsiao establish the asymptotic theory of the local linear estimator of a nonparametric cointegration ing least squares cross validation to select smoothing parameters,they demonstrate substantial finite sample efficiency gains of the local linear estimator over the local constant estimator in the simulation study.Martins-Filho,Yao and Torero consider two stage estimation for a high order conditional quantile.Utilizing thefirst stage nonparametric regression residual,they estimate the tail and quantile of condi-tional distribution by extreme value theory to approximate the tail distribution with a generalized Pareto distribution.They obtain the asymptotic properties of the estimator and illustrate their implementation andfinite sample perfor-mance in a simulation study.Gao,Liu and Racine propose an estimator for the partially linear model forβ−mixing time series data,where both continuous and categorical varaibles can appear in the nonparametric component.The authors establish their asymptotic distributions and demonstrate that the estimators can outperform existing specifications in simulations.They also provided an application using SIPP data to model a dynamic labor supply function.Gu,Li and Yang obtain explicit leading bias terms for the local polynomial estimator in a general nonparametric multivariate regression model,under smoother con-ditions on the unknown regression function.The results can be used to obtain optimal smoothing parameters in local polynomial estimation of the unknown conditional mean and derivative functions.4Hypothesis testing.Five papers are found in this category.Du and Escanciano propose a test for the serial independence of estimated residuals in location-scale models,and the test statistics have the same asymptotic distributions as the ones with true errors. They construct a generalized spectral test,and show it to be asymptotically distribution-free and powerful against any type of pairwise dependence at all lags.Simulations validate theoreticalfindings.Phillips and Lee develop limit theory for nonstationary vector autoregression(VAR)with mixed roots in the vicinity of unity involving persistent and explosive components.They further consider statistical tests for common roots and model selection for discriminat-ing roots.The results can be used to distinguish mildly explosive roots from roots that are local to unity and for testing commonality in persistence.Su,Tu and Ullah consider testing additive error structure in nonparametric structural models,against the alternative that the error enters the model nonadditively. The test statistic is motivated by the fact that the partial derivative of the non-parametric structural function with respect to the error is one under additivity.4They establish the test’s asymptotic properties and propose a bootstrap version of the test.Simulations show that the test has proper size and reasonable power infinite samples.Pesaran considers tests for errors in a panel data model to be weakly cross sectionally dependent,using the exponent of cross sectional de-pendence(CD).It is shown that the implicit null of the CD test depends on the relative expansion rates of N and T.In large N panels,the null of weak depen-dence is more appropriate than independence.With symmetric errors,the test has a standard normal distribution.The Monte Carlo evidence demonstrates the test to be a simple and powerful test of weak CD in both static and dynamic panels.Zhang,Barassi and Tan propose a residual based approach to test for the null of no cointegration against a fractional alternative which relies on the Exact Local Whittle Estimator.They compare its performance to other resid-ual based tests for fractional cointegration,and investigate the term structure of interest rates in the UK and US,concluding that the term spread is indeed a mean reverting process with long memory.5Parametric methods in constructing common factors and estimating conditional variance. The last category consists of two papers.Ng reviews and explores various ma-trix decomposition based methods for estimating common factors.The methods are extended to analyze categorical data,which involves quantifying the ordinal and nominal variables.Interestingly,the factor space can be quite precisely estimated directly from categorical data without quantification.Galbraith, Zinde-Walsh and Zhu estimate the GARCH model parameters using auxiliary information on latent variance.They obtain consistent estimates of the infinite ARCH representation parameters via a regression using the estimated quadratic variation.The GARCH parameters are estimated with a minimum distance es-timator based on estimated ARCH parameters.They show the consistency and asymptotic normality with LAD estimation of truncated ARCH approxi-mations.The simulations illustrate that the ARCH-regression estimators may be competitive with QML,and potentially more precise if sufficient intra-day information is available.References1.Badi H.Baltagi,Ying Deng,“EC3SLS Estimator for a Simultaneous Sys-tem of Spatial Autoregressive Equations with Random Effects.”2.Zongwu Cai,Linna Chen,and Ying Fang,“Semiparametric Estimation ofPartially Varying-Coefficient Dynamic Panel Data Models.”3.Keisuke Hirano,Jack R.Porter,“Location Properties of Point Estimatorsin Linear Instrumental Variables and Related Models.”4.Juan Carlos Escanciano,Lin Zhu,“A Simple Data-Driven Estimator forthe Semiparametric Sample Selection Model.”55.Yan Dong,Li Gan and Yingning Wang,“Residential Mobility,Neighbor-hood Effects,and Educational Attainment of Blacks and Whites.”6.Chunrong Ai,Meixia Meng,“Endogeneity in Semiparametric Panel Bi-nary Choice Model.”7.Yanqin Fan and Ruixuan Liu,“Symmetrized Multivariate k-NN Estima-tors.”8.Patrick W.Saart,Jiti Gao,David E.Allen,“Semiparametric Autoregres-sive Conditional Duration Model:Theory and Practice.”9.Zhongwen Liang,Zhongjian Lin,Cheng Hsiao,“Local Linear Estimationof a Nonparametric Cointegration Model.”10.Carlos Martins-Filho,Feng Yao,Maximo Torero,“High Order ConditionalQuantile Estimation Based on nonparametric Models of Regression.”11.Qi Gao,Long Liu,Jeffrey S.Racine,“A Partially Linear Kernel Estimatorfor Categorical Data.”12.Jingping Gu,Qi Li,Jui-Chung Yang,“Multivariate Local Polynomial Ker-nel Estimators:Leading Bias and Asymptotic Distribution.”13.Zaichao Du,Juan Carlos Escanciano,“Nonparametric Distribution-FreeTest for Serial Independence of Errors.”14.Peter C.B.Phillips,Ji Hyung Lee,“Limit Theory for VARs with MixedRoots Near Unity.”15.Liangjun Su,Yundong Tu,Aman Ullah,“Testing Additive Separability ofError Term in Nonparametric Structural Models.”16.M.Hashem Pesaran,“Testing Weak Cross-Sectional Dependence in LargePanels.”17.Dayong Zhang,Marco R.Barassi,Jijun Tan,“Residual based tests forfractional cointegration:testing the term structure of interest rates.”18.Serena Ng,“Constructing Common Factors from Continuous and Cate-gorical Data.”19.John W.Galbraith,Victoria Zinde-Walsh and Jingmei Zhu,“GARCHModel Estimation Using Estimated Quadratic Variation.”6。

A Local Generalized Method of Moments EstimatorArthur Lewbel∗Boston CollegeJune2006AbstractA local Generalized Method of Moments Estimator is proposed for nonparametrically estimatingunknown functions that are defined by conditional moment restrictions.JEL Codes:C14,C13.Keywords:Generalized Method of Moments,Nonparametric Estimation,Semiparametric Estimation,Conditional Moments.Assume we observe a sample of observations of a random vector W.Let Z and X be random subvectors of W,so each contains some or all of the elements of W.Hansen’s(1982)Generalized Method of Moments (GMM)estimates a vector of parametersθfrom unconditional moments E d g(θ0,W)e=0given a known vector valued function g.Asymptotically efficient estimates ofθgiven conditional moments E[g(θ,W)|Z=z)]=0can be obtained using variants of GMM or empirical likelihood such as Newey(1993), Donald,Imbens,and Newey(2003),Otsu(2003),or Dominguez and Lobato(2004).Suppose that,in place of a parameter vectorθ,the goal is estimation of a vector of unknown functions q(X)where E[g(q0(X),W)|Z=z)]=0.Resulting nonparametric conditional moment estimators include Carrasco and Florens(2000),Newey and Powell(2003),and Ai and Chen(2003).These estimators require verification of relatively elaborate sets of regularity conditions.∗Department of Economics,Boston College,140Commonwealth Avenue,Chestnut Hill,MA02467USA.Tel:(617)-552-3678fax:(617)-552-2308email:lewbel@ url:/~lewbel1This paper focuses on the special case of the general nonparametric conditional moment problem where X and Z are the same,so we wish to estimate unknown functions q(Z)whereE[g(q0(Z),W)|Z=z)]=0.(1)While estimators such as Ai and Chen(2003)and other can be applied in this case,the local GMM estimator proposed here exploits the assumption that the unknown functions q depend on the same variables as the conditional moments,resulting in a short,simple set of regularity conditions.This local GMM estimator is straighforward to implement and is a natural extension of ordinary GMM estimation of the same model when Z is discrete.An example application is the nonparametric probit model W=I[q0(Z)+e≥0],where I()denotes the indicator function that equals one if its argument is true and zero otherwise,q0(z)is an unknown function to be estimated,and e is a standard normal independent of Z,or has some other known distribution.Then estimation could be based on equation(1)where the function g is g(q,w)=w−F e(q)where F e is the known cumulative distribution function of−e.Nonparametric censored or truncated regression would have a similar form.The local gmm estimator could also be used for estimation of Euler equations,which are mean zero conditional on information in a given time period,and may have parameters q0(z),such as preference parameters,that are unknown functions of observables.Another application is Lewbel(2006), who provides examples of a treatment model that generates conditional moments in the form of equation (1).The local GMM estimator provided here is very similar to the local nonlinear least squares estimator of Gozalo and Linton(2000),and in fact an early draft of their paper included a GMM variant.In their applications a local version of a parametric model is estimated,which converges at rate root n if the model is correct,but remains consistent as a nonparametric regression if the parametric model is misspecified (analogous to local polynomial regression,which is the special case of their estimator in which the para-metric model is a polynomial).In the present paper no parametric model is proposed.Instead,the intended estimand from the outset is the unknown vector of functions q0(z).To motivate the estimator,considerfirst the case where Z is discretely distributed,or more specifically, that Z has one or more mass points and we only wish to estimate q0(z)at those points.Letθz0=q0(z).If the distribution of Z has a mass point with positive probability at z,thenE[g(θz,W)I(Z=z)]E[g(θz,W)|Z=z]=2so equation(1)holds if and only if E[g(θz0,W)I(Z=z)]=0.It therefore follows that ifθz0is identified from the moment conditions(1),then we may under standard regularity conditions estimateθz0=q0(z)bythe ordinary GMM estimatorEθz=arg minθz n;i=1g(θz,W i) I(Z i=z) n n;i=1g(θz,W i) I(Z i=z)(2)for some sequence of positive definite n.If n is a consistent estimator of z0=E[g(θz0,W)g(θz0,W) I(Z= z)]−1,then standard efficient GMM gives√n(Eθz−θz0)→d N 0,v E t∂g(θz0,W)I(Z=z)∂θz u z0E t∂g(θz0,W)I(Z=z)∂θz uw−1Continue to assume that equation(1)holds and identifies q0(z)where g is known and q0is unknown, but now assume that Z is continuously distributed.The proposed local GMM estimator consists of applying equation(2)to this case of continuous Z by replacing averaging over just observations Z i=z with local averaging over observations Z i in the neighborhood of z.Assumption A1.Let Z i,W i,i=1,...,n,be an independently,identically distributed random sample of observations of the random vectors Z,W.The d vector Z is continuously distributed with density function f(Z).For given point z in the interior of supp(Z)having f(z)>0and a given vector valued function g(q,w)where g(q(z),w)is twice differentiable in the vector q(z)for all q(z)in some compact set (z), there exists a unique q0(z)∈ (z)such that E[g(q0(z),W)|Z=z]=0.Let n be afinite positive definite matrix for all n,as is =plim n→∞ n.Assumption A1provides the required moment condition structure and identification for the model,and Assumption A2below provides conditions for local averaging.Defineε[q(z),W],V(z),and R(z)by ε[q(z),W]=g(q(z),W)f(z)−E[g(q(z),W)f(Z)|Z=z]V(z)=E dε(q0(z),W)ε(q0(z),W)T|Z=z eR(z)=E t∂g[q0(z),W]∂q0(z)Tf(Z)|Z=z uAssumption A2.Letηbe some constant greater than2.Let K be a nonnegative symmetric kernel func-tion satisfying5K(u)du=1and5||K(u)||ηdu isfinite.For all q(z)∈ (z),E[||g(q(z),W)f(Z)||η|3Z=z],V(z),R(z),and V ar[[∂g(q(z),W)/∂q(z)]f(Z)|Z=z]arefinite and continuous at z andE[g(q(z),W)f(Z)|Z=z]isfinite and twice continuously differentiable at z.DefineS n(q(z))=1n;i=1g[q(z),W i]K t z−Z i uwhere b=b(n)is a bandwidth parameter.The proposed local GMM estimator isE q(z)=arg inf q(z)∈ (z)S n(q(z))T n S n(q(z))(3)THEOREM1:Given Assumptions A1and A2,if the bandwidth b satisfies nb d+4→0and nb d→∞,then E q(z)is a consistent estimator of q0(z)with limiting distribution(nb)1/2[E q(z)−q0(z)]→d N v0,(R(z)T R(z))−1R(z)T V(z) R(z)(R(z)T R(z))−1=K(u)2du]wTheorem1assumes a bandwidth rate that makes bias shrink faster than variance,and so is not meansquare optimal.One could instead choose the mean square optimal rate where nb d+4goes to a constant,but the resulting bias term would then have a complicated form that depends on the kernel regression biasesin both S n(q0(z))and its derivative with respect to q0(z),among other terms.Applying the standard two step GMM procedure,we mayfirst estimate H q(z)=arg inf q(z)∈ (z)S n(q(z))T S n(q(z)), then let n be the inverse of the sample variance of S n(H q(z))to get =V(z)−1,making(nb)1/2[E q(z)−q0(z)]→d N v0,(R(z)T R(z))−1=K(u)2du]wwhere R(z)can be estimated usingR n(z)=1n;i=1∂g[E q(z),W i]∂q(z)K t z−Z i uAt the expense of some additional notation,the two estimators(2)and(3)can be combined to handle Z containing both discrete and continuous elements,by replacing the kernel function in S n with the product of a kernel over the continuous elements and an indicator function for the discrete elements.4PROOF OF THEOREM1:DefineS n(q(z))=∂S n(q(z))∂q(z)T=1dn;i=1∂g[q(z),W i]∂q(z)TK t z−Z i uQ n(q(z))=S n(q(z))T n S n(q(z))Let S0(q(z))=plim n→∞S n(q(z))and similarly for S n and Q n.Assumptions A1and A2give sufficient conditions for consistency of these kernel estimators,so these probability limits exist andS0(q(z))=E[g(q(z),W)f(z)|Z=z]Q0(q(z))=S0(q(z))T S0(q(z)).Now consider consistency of E q(z).We have pointwise convergence of S n(q(z))to S0(q(z))and compact-ness of (z).It is also the case that|S n(q(z))|=O p(1),since|S n(q(z))|is a kernel estimator,and standard conditions have been provided for its consistency,that is,plim|S n(q(z))|=E[|∂g(q(z),W)/∂q(z)|f(Z)| Z=z].This suffices for stochastic equicontinuity,and therefore we have the uniform convergenceplim supq(z)∈ (z)|S n(q(z))−S0(q(z))|=0.It follows that Q n(q(z))also converges uniformly to Q0(q(z)).The assumptions provide compactness of (z)and imply continuity of Q0(q).The quadratic form of Q0is uniquely maximized at S0(q0(z))=0 and hence at q(z)=q0(z),so the standard conditions for consistency plim E q(z)=q0(z)are satisfied.For the limiting distribution,Taylor expanding thefirst order conditions as in standard GMM givesS n(E q(z))T n d S n(q0(z))+S n(H q(z))(E q(z)−q0(z))e=0where H q(z)lies between E q(z)and q0(z).By consistency of E q,the uniform convergence of S n,and using R(z)=S 0(q0(z)),this simplifies toR(z)T d S n(q0(z))+R(z)(E q(z)−q0(z))e=o p(1)Solving for E q(z)−q0(z)and multiplying by(nb)1/2gives(nb)1/2(E q(z)−q0(z))=(R(z)T R(z))−1R(z)T (nb)1/2S n(q0(z))+o p((nb)1/2).5Now S0(q0(z))=0and standard kernel regression limiting distribution theory gives(nb)1/2S n(q0(z))→d N[0,V(z)=K(u)2du]and the theorem follows.ReferencesAi,C.and X.Chen(2003),"Efficient Estimation of Models With Conditional Moment Restrictions Containing Unknown Functions,"Econometrica,71,1795-1844.Carrasco,M.and J.P.Florens(2000),"Generalization of GMM to a Continuum of Moment Conditions," Econometric Theory,16,797-834.Dominguez,M.and I.Lobato,(2004),"Consistent Estimation of Models Defined by Conditional Mo-ment Restrictions,"Econometrica,72,1601-1615.Donald,S.G.,G.W.Imbens,and W.K.Newey(2003),"Empirical Likelihood Estimation and Consis-tent Tests With Conditional Moment Restrictions,"Journal of Econometrics,117,55-93.Florens,J.-P.and L.Malavolti(2003),"Instrumental Regression with Discrete Variables,"unpublished manuscript..Hansen,L.,(1982),"Large Sample Properties of Generalized Method of Moments Estimators,"Econo-metrica,50,1029-1054.Lewbel,A.,(2006),"Estimation of Average Treatment Effects With Misclassification,"Econometrica, forthcoming.Newey,W.K.(1993),"Efficient Estimation of Models With Conditional Moment Restrictions,"in Handbook of Statistics,vol.11,ed.by G.S.Maddala,C.R.Rao,and H.D.Vinod,Amsterdam:North Holland,chapter16.Newey,W.K.and J.L.Powell,(2003),"Instrumental Variable Estimation of Nonparametric Models," Econometrica,711565-1578.Otsu,T.,(2003),"Penalized Empirical Likelihood Estimation of Conditional Moment Restriction Mod-els with Unknown Functions,"unpublished manuscript.6。

——名词解释将因变量与一组解释变量和未观测到的扰动联系起来的方程，方程中未知的总体参数决定了各解释变量在其他条件不变下的效应。

与经济分析不同，在进行计量经济分析之前，要明确变量之间的函数形式。

经验分析（Empirical Analysis）：在规范的计量分析中，用数据检验理论、估计关系式或评价政策有效性的研究。

确定遗漏变量、测量误差、联立性或其他某种模型误设所导致的可能偏误的过程线性概率模型（LPM）（Linear Probability Model, LPM）：响应概率对参数为线性的二值响应模型。

没有一个模型可以通过对参数施加限制条件而被表示成另一个模型的特例的两个（或更多）模型。

有限分布滞后（FDL）模型（Finite Distributed Lag (FDL) Model）：允许一个或多个解释变量对因变量有滞后效应的动态模型。

布罗施-戈弗雷检验（Breusch-Godfrey Test）：渐近正确的AR（p）序列相关检验，以AR（1）最为流行；该检验考虑到滞后因变量和其他不是严格外生的回归元。

布罗施-帕甘检验（Breusch-Pagan Test）/（BP Test）：将OLS 残差的平方对模型中的解释变量做回归的异方差性检验。

若一个模型正确，则另一个非嵌套模型得到的拟合值在该模型是不显著的。

因此，这是相对于非嵌套对立假设而对一个模型的检验。

在模型中包含对立模型的拟合值，并使用对拟合值的t 检验来实现。

回归误差设定检验（RESET）（Regression Specification Error Test, RESET）：在多元回归模型中，检验函数形式的一般性方法。

它是对原OLS 估计拟合值的平方、三次方以及可能更高次幂的联合显著性的F 检验。

怀特检验（White Test）：异方差的一种检验方法，涉及到做OLS 残差的平方对OLS 拟合值和拟合值的平方的回归。

这种检验方法的最一般的形式是，将OLS 残差的平方对解释变量、解释变量的平方和解释变量之间所有非多余的交互项进行回归。

统计学专业英语词汇AAbsolute deviation,绝对离差Absolute number,绝对数Absolute residuals,绝对残差Acceleration array,加速度立体阵Acceleration in an arbitrary direction,任意方向上的加速度Acceleration normal,法向加速度Acceleration space dimension,加速度空间的维数Acceleration tangential,切向加速度Acceleration vector,加速度向量Acceptable hypothesis,可接受假设Accumulation,累积Accuracy,准确度Actual frequency,实际频数Adaptive estimator,自适应估计量Addition,相加Addition theorem,加法定理Additivity,可加性Adjusted rate,调整率Adjusted value,校正值Admissible error,容许误差Aggregation,聚集性Alternative hypothesis,备择假设Among groups,组间Amounts,总量Analysis of correlation,相关分析Analysis of covariance,协方差分析Analysis of regression,回归分析Analysis of time series,时间序列分析Analysis of variance,方差分析Angular transformation,角转换ANOVA（analysis of variance）,方差分析ANOVA Models,方差分析模型Arcing,弧/弧旋Arcsine transformation,反正弦变换Area under the curve,曲线面积AREG,评估从一个时间点到下一个时间点回归相关时的误差ARIMA,季节和非季节性单变量模型的极大似然估计Arithmetic grid paper,算术格纸Arithmetic mean,算术平均数Arrhenius relation,艾恩尼斯关系Assessing fit,拟合的评估Associative laws,结合律Asymmetric distribution,非对称分布Asymptotic bias,渐近偏倚Asymptotic efficiency,渐近效率Asymptotic variance,渐近方差Attributable risk,归因危险度Attribute data,属性资料Attribution,属性Autocorrelation,自相关Autocorrelation of residuals,残差的自相关Average,平均数Average confidence interval length,平均置信区间长度Average growth rate,平均增长率BBar chart,条形图Bar graph,条形图Base period,基期Bayes theorem, 贝叶斯定理Bell-shaped curve,钟形曲线Bernoullidistribution,伯努力分布Best-trim estimator,最好切尾估计量Bias,偏性Binary logistic regression,二元逻辑斯蒂回归Binomial distribution,二项分布Bisquare,双平方Bivariate Correlate,二变量相关Bivariate normal distribution,双变量正态分布Bivariate normal population,双变量正态总体Biweight interval,双权区间Biweight M-estimator,双权M 估计量Block,区组/配伍组BMDP(Biomedical computer programs),BMDP 统计软件包Box plots,箱线图/箱尾图Break down bound,崩溃界/崩溃点CCanonical correlation,典型相关Caption,纵标目Case-control study,病例对照研究Categorical variable,分类变量Catenary,悬链线Cauchy distribution,柯西分布Cause-and-effect relationship,因果关系Cell,单元Censoring,终检Center of symmetry,对称中心Centering and scaling,中心化和定标Central tendency,集中趋势Central value,中心值CHAID-χ2AutomaticInteractionDetector,卡方自动交互检测Chance,机遇Chance error,随机误差Chance variable,随机变量Characteristic equation,特征方程Characteristic root,特征根Characteristic vector,特征向量Chebshev criterion of fit,拟合的切比雪夫准则Chernoff faces,切尔诺夫脸谱图Chi-square test,卡方检验/χ2 检验Choleskey decomposition,乔洛斯基分解Circle chart,圆图Class interval,组距Class mid-value,组中值Class upper limit,组上限Classified variable,分类变量Cluster analysis,聚类分析Cluster sampling,整群抽样Code,代码Coded data,编码数据Coding,编码Coefficient of contingency,列联系数Coefficientof determination,决定系数Coefficient ofmultiple correlation,多重相关系数Coefficient ofpartial correlation,偏相关系数Coefficient of production-moment correlation,积差相关系数Coefficient of rank correlation,等级相关系数Coefficient of regression,回归系数Coefficient of skewness,偏度系数Coefficient of variation,变异系数Cohort study,队列研究Column,列Column effect,列效应Column factor,列因素Combination pool,合并Combinative table,组合表Common factor,共性因子Common regression coefficient,公共回归系数Common value,共同值Common variance,公共方差Common variation,公共变异Communality variance,共性方差Comparability,可比性Comparison of bathes,批比较Comparison value,比较值Compartment model,分部模型Compassion,伸缩Complement of an event,补事件Complete association,完全正相关Complete dissociation,完全不相关Complete statistics,完备统计量Completely randomized design,完全随机化设计Composite event,联合事件/复合事件Concavity,凹性Conditional expectation,条件期望Conditional likelihood,条件似然Conditional probability,条件概率Conditionally linear,依条件线性Confidence interval,置信区间Confidence limit,置信限Confidence lower limit,置信下限Confidence upper limit,置信上限Confirmatory Factor Analysis,验证性因子分析Confirmatory research,证实性实验研究Confounding factor,混杂因素Conjoint,联合分析Consistency,相合性Consistency check,一致性检验Consistent asymptotically normal estimate,相合渐近正态估计Consistent estimate,相合估计Constrained nonlinear regression,受约束非线性回归Constraint,约束Contaminated distribution,污染分布Contaminated Gausssian,污染高斯分布Contaminated normal distribution,污染正态分布Contamination,污染Contamination model,污染模型Contingency table,列联表Contour,边界线Contribution rate,贡献率Control,对照Controlled experiments,对照实验Conventional depth,常规深度Convolution,卷积Corrected factor,校正因子Corrected mean,校正均值Correction coefficient,校正系数Correctness,正确性Correlation coefficient,相关系数Correlation index,相关指数Correspondence, 对应Counting,计数Counts,计数/频数Covariance,协方差Covariant,共变Cox Regression, Cox 回归Criteria for fitting,拟合准则Criteria of least squares,最小二乘准则Critical ratio,临界比Critical region,拒绝域Critical value,临界值Cross-over design,交叉设计Cross-section analysis,横断面分析Cross-section survey,横断面调查Cross tabs,交叉表Cross-tabulation table,复合表Cube root,立方根Cumulative distribution function,累计分布函数Cumulative probability,累计概率Curvature,曲率/弯曲Curve fit,曲线拟和Curve fitting,曲线拟合Curvilinear regression,曲线回归Curvilinear relation,曲线关系Cut-and-try method,尝试法Cycle,周期Cyclist,周期性DD test, D 检验Data acquisition,资料收集Databank,数据库Data capacity,数据容量Data deficiencies,数据缺乏Data handling,数据处理Data manipulation,数据处理Data processing,数据处理Data reduction,数据缩减Data set,数据集Data sources,数据来源Data transformation,数据变换Data validity,数据有效性Data-in,数据输入Data-out,数据输出Dead time,停滞期Degree of freedom,自由度Degree of precision,精密度Degree of reliability,可靠性程度Degression,递减Density function,密度函数Density of datapoints,数据点的密度Dependent variable,应变量/依变量/因变量Depth,深度Derivative matrix,导数矩阵Derivative-free methods,无导数方法Design,设计Determinacy,确定性Determinant,行列式Determinant,决定因素Deviation,离差Deviation from average,离均差Diagnostic plot,诊断图Dichotomousvariable,二分变量Differentialequation,微分方程Directstandardization,直接标准化法Discrete variable,离散型变量Discriminant,判断Discriminant analysis,判别分析Discriminant coefficient,判别系数Discriminant function,判别值Dispersion,散布/分散度Disproportional,不成比例的Disproportionate sub-class numbers,不成比例次级组含量Distribution free,分布无关性/免分布Distribution shape,分布形状Distribution-free method,任意分布法Distributive laws,分配律Disturbance,随机扰动项Dose response curve,剂量反应曲线Double blind method,双盲法Doubleblind rial,双盲试验Double exponential distribution,双指数分布Double logarithmic,双对数Downward rank,降秩Dual-space plot,对偶空间图DUD,无导数方法Duncan's new multiple range method,新复极差法/Duncan 新法EEffect, 实验效应Eigen value,特征值Eigen vector,特征向量Ellipse,椭圆Empirical distribution,经验分布Empirical probability,经验概率单位Enumeration data,计数资料Equal sun-class number,相等次级组含量Equally likely,等可能Equal variance,同变性Error,误差/错误Error of estimate,估计误差Error type I,第一类错误Error type II,第二类错误Estimand,被估量Estimated error mean squares,估计误差均方Estimated error sum of squares,估计误差平方和Euclidean distance,欧式距离Event,事件Exceptional data point,异常数据点Expectation plane,期望平面Expectation surface,期望曲面Expected values,期望值Experiment,实验Experimental sampling,试验抽样Experimental unit,试验单位Explanatory variable,说明变量/解释变量Exploratory data analysis,探索性数据分析Explore Summarize,探索-摘要Exponential curve,指数曲线Exponential growth,指数式增长Exsooth,指数平滑方法Extended fit,扩充拟合Extra parameter,附加参数Extra polation,外推法Extreme observation,末端观测值Extremes,极端值/极值FF distribution, F 分布F test, F 检验Factor,因素/因子Factor analysis,因子分析Factor score,因子得分Factorial,阶乘Factorial design,析因试验设计False negative,假阴性False negative error,假阴性错误Family of distributions,分布族Family of estimators,估计量族Fanning,扇面Fatality rate,病死率Field investigation,现场调查Field survey,现场调查Finitepopulation,有限总体Finite-sample, 有限样本Firstderivative,一阶导数First principal component,第一主成分First quartile,第一四分位数Fisher information,费雪信息量Fitted value,拟合值Fitting a curve,曲线拟合Fixed base,定基Fluctuation,随机起伏Forecast,预测Four fold table,四格表Fourth, 四分点Fraction blow,左侧比率Fractional error,相对误差Frequency,频率Frequency polygon,频数多边图Frontier point,界限点Function relationship,泛函关系GGamma distribution,伽玛分布Gauss increment,高斯增量Gaussian distribution,高斯分布/正态分布Gauss-Newton increment,高斯-牛顿增量General census,全面普查GENLOG(Generalized liner models),广义线性模型Geometric mean,几何平均数Gini's mean difference,基尼均差GLM(General liner models),通用线性模型Goodness of fit,拟和优度/配合度Gradientof determinant,行列式的梯度Graeco-Latin square,希腊拉丁方Grand mean,总均值Gross errors,重大错误Gross-error sensitivity,大错敏感度Group averages,分组平均Grouped data,分组资料Guessed mean,假定平均数HHalf-life,半衰期Hampel M-estimators,汉佩尔M 估计量Happenstance,偶然事件Harmonic mean,调和均数Hazard function,风险均数Hazard rate,风险率Heading,标目Heavy-tailed distribution,重尾分布Hessian array,海森立体阵Heterogeneity,不同质Heterogeneity of variance,方差不齐Hierarchical classification,组内分组Hierarchical clustering method,系统聚类法High-leverage point,高杠杆率点HILOGLINEAR,多维列联表的层次对数线性模型Hinge,折叶点Histogram,直方图Historical cohort study,历史性队列研究Holes,空洞HOMALS,多重响应分析Homogeneity of variance,方差齐性Homogeneity test,齐性检验Huber M-estimators,休伯M 估计量Hyperbola,双曲线Hypothesis testing,假设检验Hypothetical universe,假设总体IImpossible event,不可能事件Independence,独立性Independent variable,自变量Index,指标/指数Indirect standardization,间接标准化法Individual,个体Inference band, 推断带Infinite population,无限总体Infinitely great, 无穷大Infinitely small,无穷小Influence curve,影响曲线Information capacity,信息容量Initial condition,初始条件Initial estimate,初始估计值Initial level,最初水平Interaction,交互作用Interaction terms,交互作用项Intercept,截距Interpolation,内插法Inter quartile range,四分位距Interval estimation,区间估计Intervals of equal probability,等概率区间Intrinsic curvature,固有曲率Invariance, 不变性Inverse matrix,逆矩阵Inverse probability,逆概率Inverse sine transformation,反正弦变换Iteration,迭代JJacobian determinant,雅可比行列式Joint distribution function,联合分布函数Joint probability,联合概率Joint probability distribution,联合概率分布KK means method,逐步聚类法Kaplan-Meier,评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier 图Kendall's rank correlation, Kendall 等级相关Kinetic,动力学Kolmogorov-Smirnove test,柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal 及Wallis 检验/多样本的秩和检验/H 检验Kurtosis,峰度LLack of fit,失拟Ladder of powers,幂阶梯Lag,滞后Large sample,大样本Large sample test,大样本检验Latin square,拉丁方Latin square design,拉丁方设计Leakage,泄漏Least favorable configuration,最不利构形Least favorable distribution,最不利分布Least significant difference,最小显著差法Least square method,最小二乘法Least-absolute-residuals estimates,最小绝对残差估计Least-absolute-residuals fit,最小绝对残差拟合Least-absolute-residuals line,最小绝对残差线Legend,图例L-estimator,L 估计量L-estimator of location,位置L 估计量L-estimator of scale,尺度L 估计量Level,水平Life expectance,预期期望寿命Life table,寿命表Life table method,生命表法Light-taile distribution,轻尾分布Likelihood function,似然函数Likelihood ratio,似然比Line graph,线图Linear correlation,直线相关Linear equation,线性方程Linear programming,线性规划Linear regression,直线回归/线性回归Linear trend,线性趋势Loading,载荷Location and scale equi variance,位置尺度同变性Location equi variance,位置同变性Location invariance,位置不变性Location scale family,位置尺度族Log rank test,时序检验Logarithmic curve,对数曲线Logarithmic normal distribution,对数正态分布Logarithmic scale,对数尺度Logarithmic transformation,对数变换Logic check,逻辑检查Logistic distribution,逻辑斯蒂分布Logit transformation, Logit 转换LOGLINEAR,多维列联表通用模型Lognormal distribution,对数正态分布Lost function,损失函数Low correlation,低度相关Lower limit,下限Lowest-attained variance,最小可达方差LSD,最小显著差法的简称Lurking variable,潜在变量MMain effect,主效应Major heading,主辞标目Marginal density function,边缘密度函数Marginal probability,边缘概率Marginal probability distribution,边缘概率分布Matched data,配对资料Matched distribution,匹配过分布Matching of distribution,分布的匹配Matching of transformation,变换的匹配Mathematical expectation,数学期望Mathematical model,数学模型MaximumL-estimator,极大L 估计量Maximumlikelihood method,最大似然法Mean,均数Mean squares between groups,组间均方Mean squares within group,组内均方Means (Compare means),均值-均值比较Median,中位数Median effective dose,半数效量Median lethal dose,半数致死量Median polish,中位数平滑Median test,中位数检验Minimal sufficient statistic,最小充分统计量Minimum distance estimation,最小距离估计Minimum effective dose,最小有效量Minimum lethal dose,最小致死量Minimum variance estimator,最小方差估计量MINITAB,统计软件包Minor heading,宾词标目Missing data,缺失值Model specification,模型的确定Modeling Statistics ,模型统计Models for outliers,离群值模型Modifying the model,模型的修正Modulus of continuity,连续性模Morbidity,发病率Most favorable configuration,最有利构形Multidimensional Scaling (ASCAL),多维尺度/多维标度Multinomial Logistic Regression ,多项逻辑斯蒂回归Multiple comparison,多重比较Multiple correlation ,复相关Multiple covariance,多元协方差Multiple linear regression,多元线性回归Multiple response ,多重选项Multiple solutions,多解Multiplication theorem,乘法定理Multiresponse,多元响应Multi-stage sampling,多阶段抽样Multivariate T distribution,多元T 分布Mutual exclusive,互不相容Mutual independence,互相独立NNatural boundary,自然边界Natural dead,自然死亡Natural zero,自然零Negative correlation,负相关Negative linear correlation,负线性相关Negatively skewed,负偏Newman-Keuls method, q 检验NK method, q 检验No statistical significance,无统计意义Nominal variable,名义变量Nonconstancy of variability,变异的非定常性Nonlinear regression,非线性相关Nonparametric statistics,非参数统计Nonparametric test,非参数检验Normal deviate,正态离差Normal distribution,正态分布Normal equation,正规方程组Normal ranges,正常范围Normal value,正常值Nuisance parameter,多余参数/讨厌参数Null hypothesis,无效假设Numerical variable,数值变量OObjective function,目标函数Observation unit,观察单位Observed value, 观察值One sided test,单侧检验One-way analysis of variance,单因素方差分析One way ANOVA ,单因素方差分析Open sequential trial,开放型序贯设计Optrim, 优切尾Optrim efficiency,优切尾效率Order statistics,顺序统计量Ordered categories,有序分类Ordinal logistic regression ,序数逻辑斯蒂回归Ordinal variable,有序变量Orthogonal basis,正交基Orthogonal design,正交试验设计Orthogonality conditions,正交条件ORTHOPLAN,正交设计Outlier cutoffs,离群值截断点Outliers,极端值OVERALS ,多组变量的非线性正规相关Overshoot,迭代过度PPaired design,配对设计Paired sample,配对样本Pairwise slopes,成对斜率Parabola,抛物线Parallel tests,平行试验Parameter,参数Parametric statistics,参数统计Parametric test,参数检验Partial correlation,偏相关Partial regression,偏回归Partial sorting,偏排序Partials residuals,偏残差Pattern,模式Pearson curves,皮尔逊曲线Peeling,退层Percent bar graph,百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves,百分位曲线Periodicity,周期性Permutation,排列P-estimator,P 估计量Pie graph,饼图Pitman estimator,皮特曼估计量Pivot,枢轴量Planar,平坦Planar assumption,平面的假设PLANCARDS,生成试验的计划卡Point estimation,点估计Poisson distribution,泊松分布Polishing,平滑Polled standard deviation,合并标准差Polled variance,合并方差Polygon,多边图Polynomial,多项式Polynomial curve,多项式曲线Population,总体Population attributable risk,人群归因危险度Positive correlation,正相关Positively skewed,正偏Posterior distribution,后验分布Power of a test,检验效能Precision,精密度Predicted value,预测值Preliminary analysis,预备性分析Principalcomponent analysis,主成分分析Priordistribution,先验分布Prior probability,先验概率Probabilistic model,概率模型probability,概率Probability density,概率密度Product moment,乘积矩/协方差Profile trace,截面迹图Proportion,比/构成比Proportion allocation in stratified random sampling,按比例分层随机抽样Proportionate,成比例Proportionate sub-class numbers,成比例次级组含量Prospective study,前瞻性调查Proximities, 亲近性Pseudo F test,近似F 检验Pseudo model,近似模型Pseudo sigma,伪标准差Purposive sampling,有目的抽样QQR decomposition, QR 分解Quadratic approximation,二次近似Qualitative classification,属性分类Qualitative method,定性方法Quantile-quantile plot,分位数-分位数图/Q-Q 图Quantitative analysis,定量分析Quartile,四分位数Quick Cluster,快速聚类RRadix sort,基数排序Random allocation,随机化分组Random blocks design,随机区组设计Random event,随机事件Randomization,随机化Range,极差/全距Rank correlation,等级相关Rank sum test,秩和检验Rank test,秩检验Ranked data,等级资料Rate,比率Ratio,比例Raw data,原始资料Rawresidual,原始残差Rayleigh's test,雷氏检验Rayleigh's Z,雷氏Z 值Reciprocal,倒数Reciprocal transformation,倒数变换Recording,记录Redescending estimators,回降估计量Reducing dimensions,降维Re-expression,重新表达Reference set,标准组Regionof acceptance,接受域Regression coefficient,回归系数Regression sum of square,回归平方和Rejection point,拒绝点Relative dispersion,相对离散度Relative number,相对数Reliability,可靠性Reparametrization,重新设置参数Replication,重复Report Summaries,报告摘要Residual sum of square,剩余平方和Resistance,耐抗性Resistant line,耐抗线Resistant technique,耐抗技术R-estimator of location,位置R 估计量R-estimator of scale,尺度R 估计量Retrospective study,回顾性调查Ridge trace,岭迹Ridit analysis , Ridit 分析Rotation, 旋转Rounding,舍入Row,行Row effects,行效应Row factor,行因素RXC table, RXC 表SSample,样本Sample regression coefficient,样本回归系数Sample size,样本量Sample standard deviation,样本标准差Sampling error,抽样误差SAS(Statistical analysis system ),SAS 统计软件包Scale,尺度/量表Scatter diagram,散点图Schematic plot,示意图/简图Score test,计分检验Screening,筛检SEASON, 季节分析Second derivative,二阶导数Second principal component,第二主成分SEM (Structural equation modeling),结构化方程模型Semi-logarithmic graph,半对数图Semi-logarithmic paper,半对数格纸Sensitivity curve,敏感度曲线Sequential analysis,贯序分析Sequential data set,顺序数据集Sequential design,贯序设计Sequential method,贯序法Sequential test,贯序检验法Serial tests,系列试验Short-cut method,简捷法Sigmoid curve, S 形曲线Sign function,正负号函数Sign test,符号检验Signed rank,符号秩Significance test,显著性检验Significant figure,有效数字Simple cluster sampling,简单整群抽样Simple correlation,简单相关Simple random sampling,简单随机抽样Simple regression,简单回归simple table,简单表Sine estimator,正弦Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skeweddistribution, 偏斜分布Skewness,偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS 统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwiseregression, 逐步回归Storage,存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t 化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival,生存分析Survival rate,生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Test(检验)Test of linearity, 线性检验Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Timeseries, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Twosided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α 错误TypeII error, 二类错误/β 错误UMVU, 方差一致最小无偏估计简称Unbiasedestimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Unweightedleast squares, 未加权最小平方法Upper limit,上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W 检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran 检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W 估计量W-estimation of location, 位置W 估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z 检验Zero correlation, 零相关Z-transformation, Z 变换。