Lecture 17 Asymptotic normality

Lecture 17 Asymptotic normality - Economics 326 Methods of...

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Economics 326 Methods of Empirical Research in Economics Lecture 17: Asymptotic normality Vadim Marmer University of British Columbia May 5, 2010

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Why do we need asymptotic normality? I In the previous lectures, we have shown that the OLS estimator has an exact normal distribution when the errors are normally distributed. I The same assumption is needed to show that the T statistic has a t -distribution and the F statistic has an F -distribution. I In this lecture, we will argue that even when the errors are not normally distributed, the OLS estimator has an approximately normal distribution in large samples, provided that some additional conditions hold. I This property is used for hypothesis testing: in large samples, the T statistic has a standard normal distribution and the F statistic has a χ 2 distribution (approximately). 1/13
Asymptotic normality I Let W n be a sequence of random variables indexed by the sample size n . I Typically, W n will be a function of some estimator. For example, we will have W n = p n ˆ β n β ± . I We say that W n has an asymptotically normal distribution if its CDF converges to a normal CDF. I

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Lecture 17 Asymptotic normality - Economics 326 Methods of...

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