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Unformatted text preview: Large Sample Theory: Lecture XIV Charles B. Moss October 3, 2010 Charles B. Moss () Large Sample Theory October 3, 2010 1 / 13 1 Basic Sample Theory 2 Modes of Convergence Charles B. Moss () Large Sample Theory October 3, 2010 2 / 13 Basic Sample Theory The problems set up is that we want to discuss sample theory. I First assume that we want to make an inference, either estimation or some test, based on a sample. I We are interested in how well parameters or statistics based on that sample represent the parameters or statistics of the whole population. The complete statistical term is known as convergence. I Specifically, we are interested in whether or not the statistics calculated on the sample converge toward the population estimates. I Let { X n } be a sequence of samples. We want to demonstrate that statistics based on { X n } converge toward the population statistics for X . Charles B. Moss () Large Sample Theory October 3, 2010 3 / 13 Taking a slightly different tack: The classical assumptions for ordinary least squares (OLS) as presented in White, Halbert Asymptotic Theory for Econometricians. I Theorem 1.1 : The following are the assumptions of the classical linear model F The model is known to be y = X β + , β < ∞ ....
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 Spring '10
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 Normal Distribution, Probability theory, large sample theory, Charles B. Moss

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