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Unformatted text preview: ECON 103, Lecture 3: Statistics Review (contd.) Maria Casanova April 7th (version 1) Maria Casanova Lecture 3 Requirements for this lecture: Chapter 2 and beginning of chapter 3 of Stock and Watson Maria Casanova Lecture 3 1. Estimators An estimator ˆ θ of a parameter θ is a function of the random variables in the sample: ˆ θ = h ( X 1 , X 2 ,..., X n ) Therefore, the estimator itself is a random variable , and will have a distribution. The sampling distribution will typically vary with sample size n . Characterizing the sample distribution: Finitesample distribution: In some cases, we will be able to derive the exact sampling distribution for any sample size n . Asymptotic distribution: Other times we are only able to establish what the sampling distribution looks like as n → ∞ Maria Casanova Lecture 3 1. Estimators Figure: Sampling distribution of ˆ μ x for different sample sizes when X ∼ N (6 , . 09) .5 1 1.5 5 5.5 6 6.5 7 n=1 (a) n=1 .5 1 1.5 2 5 5.5 6 6.5 7 n=1 n=10 (b) n=10 Maria Casanova Lecture 3 1. Estimators Figure: Sampling distribution of ˆ μ x for different sample sizes when X ∼ N (6 , . 09) 1 2 3 4 5 5.5 6 6.5 7 n=1 n=10 n=50 (a) n=50 2 4 6 8 5 5.5 6 6.5 7 n=1 n=10 n=50 n=250 (b) n=250 Maria Casanova Lecture 3 1. Estimators What are the desirable characteristics of an estimator?What are the desirable characteristics of an estimator?...
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This note was uploaded on 02/04/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.
 Spring '07
 SandraBlack

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