Limiting behavior of randomly weighted averages of symmetric heavy-tailed random variables

Rasool Roozegar

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 9, 4539-4544

Abstract: In this paper we consider a sequence of independent continuous symmetric random variables X1, X2, …, with heavy-tailed distributions. Then we focus on limiting behavior of randomly weighted averages Sn = R(n)1X1 + ⋅⋅⋅ + R(n)nXn, where the random weights R(n)1, …, Rn(n) which are independent of X1, X2, …, Xn, are the cuts of (0, 1) by the n − 1 order statistics from a uniform distribution. Indeed we prove that cnSn converges in distribution to a symmetric α-stable random variable with cn = n1 − 1/α/Γ1/α(α + 1).

Date: 2017
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DOI: 10.1080/03610926.2015.1085571

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