Econometrics 10 1.1. var( ) is inversely proportional to n 1.1.1. the spread (standard deviation) of the sampling distribution is proportional to 1/ 1.1.2. Thus the sampling uncertainty associated with is proportional to 1/ (larger samples, less uncertainty, but square-root law) • The sampling distribution of when n is large (note 1-33) For small sample sizes, the distribution of will usually be complicated ( unless . . . what is true about the distribution of the Y i values in the population?) But if n is large, the sampling distribution is simple! 1.1. As n increases, the distribution of becomes more tightly centered around μ Y (the Law of Large Numbers ) 1.2. Moreover, the distribution of both become normal (the Central Limit Theorem ) 1.2.1. 1.2.2. • The Law of Large Numbers : (note 1-34) An estimator is consistent if the probability that its falls within an interval of the true population value tends to one as the sample size increases. If (
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