- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
13
Example
Population {1, 2, 3, 4} Draw samples {Y1, Y2} with sample size n=2 each time. Total possible samples {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}
17
The sampling distribution of
Y
Y is a random variable, and its properties are determined by the sampling distribution of Y
The individuals in the sample are drawn at random. Thus the values of (Y1,…, Yn) are random Thus functions of (Y1,…, Yn), such as Y , are random: had a different sample been drawn, they would have taken on a different value The distribution of Y over different possible samples of size n is called the sampling distribution of Y . The mean and variance of Y are the mean and variance of its sampling distribution, E(Y ) and var(Y ). The concept of the sampling distribution underpins all of econometrics.
14
Estimators and Estimates
Typically, we can’t observe the whole population, so we must make inferences based on the estimate from a random sample An estimator is just a mathematical formula for estimating a population parameter from sample data An estimate is the actual value the formula produces from the sample data
Econometrics
1
Econometrics
Instructor: Chui Chin Man (崔展文) Office: 511-2 (嘉庚二) E-mail: cmchui@
2
Course Requirement
Lectures: Tuesday 2:30-5:30 p.m. (Room 501嘉庚二 )
We will assume simple random sampling Choose and individual (district, entity) at random from the population Randomness and data Prior to sample selection, the value of Y is random because the individual selected is random Once the individual is selected and the value of Y is observed then Y is just a number – not random The data set is (Y1, Y2,…, Yn), where Yi = value of Y for the ith individual (district, entity) sampled
S2
2 ( Y Y ) i 1 i n
n 1
16
Estimation Y is the natural estimator of the mean. But: (a) What are the properties of Y ? (b) Why should we use Y rather than some other estimator? Y1 (the first observation) maybe unequal weights – not simple average median(Y1,…, Yn) The starting point is the sampling distribution of Y …
9
Population and Sample
Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite.
E.g. 13 billion people in China
Sample — A sample is a set of data drawn from the population. — Potentially very large, but less than the population.
15
Commonly used Estimators
We use sample mean to estimate the population mean
Y i 1Yi
n
We use sample variance to estimate the population variance
Байду номын сангаас
18
Previous example
Population {1, 2, 3, 4} population mean=2.5 Draw samples {Y1, Y2} with sample size n=2. {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4} Sample means based on the 6 samples {1.5, 2, 2.5, 2,5, 3, 3.5} is the sample distribution of Y Expected value and variance of Y ?
7
Lecture 1 Quick review of some important concepts in statistics
(Appendix C of Wooldridge)
8
Outline
Sample distribution Estimation and estimator Properties of estimator
12
Distribution of Y1,…, Yn under simple random sampling
Because individuals {Yi} are selected at random, we further make assumptions that {Yi}, i = 1,…, n, are independently distributed {Yi}, i = 1,…, n, come from the same distribution, that is, {Yi} are identically distributed That is, under simple random sampling, {Yi}, i = 1,…, n, are independently and identically distributed (i.i.d.) This framework allows rigorous statistical inferences about moments of population distributions using a sample of data from that population …
19
The mean and variance of the sampling distribution of Y
General case – that is, for Yi i.i.d. from any distribution, not just Bernoulli: 1 n 1 n 1 n mean: E(Y ) = E( Yi ) = E (Yi ) = Y = Y n i 1 n i 1 n i 1
E.g. a sample of 4 million people from Xiamen
10
Statistical Inference
Statistical inference is the process of making an estimate, prediction, or decision about a population parameter based on a sample statistic.
Grading
Assignments and computer exercises One mid-term test One final examination
10% 40% 50%
3
Textbook
Wooldridge, J. “Introductory Econometrics: A modern approach” 3 edition
