Introduction to Sampling Theory Population and Random Sample Population and Random Sample The main purpose of statistical analysis is to infer population distribution Fx(x)based on an observed data set generated from a large number of repeated ex- periments of the same kind. Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 16/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 16/167 Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Question:How to define the population if the random vari- ables X1,...,Xn in the sample are not identically distributed? The random variables X1,···,X in a random sample may not have identical probability distributions,due to the existence of heterogeneity among economic agents or structural changes of economic relationships over time. Although each Xi has a different distribution,we may assume that they may still share certain common fea- tures (e.g.,common parameter values)in their proba- bility distributions,and these common features of distri- butions can be defined as the population. Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 17/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 17/167 Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Inference of population based on a random sample is the most important feature of statistical analysis. Question: What are the requirements on the random sample? What is the best inference method given a random sam- ple? What should be done if the random sample have certain drawbacks (e.g.,sample selection bias,missing data,out- liers,etc)? Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 18/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 18/167 Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Question:How to summarize useful information in a data set x"?What is a tool to do so? Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 19/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 19/167 Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Definition 3 (6.3).[Statistic] Let Xm=(X1,...,Xn)be a random sample of size n from a population. A statistic T(X")=T(X1,...,Xn)is a real-valued or vector- valued function of a random sample X". Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 20/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 20/167 Definition 3 (6.3). [Statistic] Population and Random Sample Population and Random Sample