Lecture14-2010 - Large Sample Theory Charles B. Moss July...

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Unformatted text preview: Large Sample Theory Charles B. Moss July 22, 2010 I. Basic Sample Theory A. The problems set up is that we want to discuss sample theory. 1. First assume that we want to make an inference, either esti- mation or some test, based on a sample. 2. We are interested in how well parameters or statistics based on that sample represent the parameters or statistics of the whole population. B. The complete statistical term is known as convergence. 1. Specifically, we are interested in whether or not the statis- tics calculated on the sample converge toward the population estimates. 2. Let { X n } be a sequence of samples. We want to demon- strate that statistics based on { X n } converge toward the population statistics for X . C. Taking a slightly different tack: The classical assumptions for or- dinary least squares (OLS) as presented in White, Halbert Asymp- totic Theory for Econometricians. 1. Theorem 1.1 : The following are the assumptions of the clas- sical linear model (i) The model is known to be y = Xβ + , β < ∞ . (ii) X is a nonstochastic and finite n × k matrix. (iii) X X is nonsingular for all n ≤ k ....
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This note was uploaded on 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

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Lecture14-2010 - Large Sample Theory Charles B. Moss July...

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