Question: Let S^2 be the sample variance of a random sample drawn from a N(,^2) distribution. Show that the constant c = (n 1)/(n + 1)
Let S^2 be the sample variance of a random sample drawn from a N(,^2) distribution. Show that the constant c = (n 1)/(n + 1) minimizes E[(cS^2 ^2)^2]. Hence, the estimator (n + 1)^-1 x sum (Xi X)^2 of ^2 minimizes the mean square error among estimators of the form cS^2
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