Let x1; : : : ; xn be a random sample from a population

| September 10, 2018

Let x1; : : : ; xn be a random sample from a population of x with …nite fourth moments. Let xn andx2n be the sample averages of x and x2, respectively. Find constants a and b and function c(n) suchthat the vector sequencec(n)xn a x2n bconverges to a nontrivial distribution, and determine this limiting distribution. Derive the asymp-totic distribution of the sample variance x2n (xn)2 :

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