ECN 129 Lecture Notes - Variance, Continuous Mapping Theorem, Consistent Estimator
30 Oct 2012
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Assume that 2 = e[(x )2] and e[(x )4] are both. Nite, show that limn [mse( 2)] = 0: refer to question 5 from the 3rd assignment. Show that fx (x) is a consistent estimator of fx (x): consider the discrete random variable sn, with pmf. That is, calculate (1) = x1, (2) = (x1 + x2)/2, and so on, up to (5000) = (x1 + . Plot the 5000 values of (i) (on the vertical axis) against the 5000 values of i (on the horizontal axis). Add a horizontal line corresponding to = e(x). Explain what is happening here: randomly generate one million samples of n = 5 iid observations on x u (0, 1), calculating the sample mean, , for each sample. Using your one million values of , estimate e( ) and var( ) (i. e. , calculate the sample mean and sample variance of your one million values of ).
