On the quadratic moment of self-normalized sums

Fredrik Jonsson

Statistics & Probability Letters, 2010, vol. 80, issue 17-18, 1289-1296

Abstract: Let an integer n>=2 and a vector of independent, identically distributed random variables X1,...,Xn be given with and define the self-normalized sum . With a formula for we prove that and that if and only if the summands are symmetrically distributed. We also construct examples where Zn converges to the standard normal distribution as n tends to infinity while tends to infinity (the distribution of the summands varies with n).

Keywords: Quadratic; moment; Self-normalization; Symmetric; distributions; Student's; t-test (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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