On convergence rates of averages of weakly dependent random variables

Gwo Dong Lin

Statistics & Probability Letters, 1993, vol. 16, issue 2, 159-162

Abstract: Let {;Xn}[infinity]n=1 be a sequence of random variabls on a probability space, r > 1 and the delayed sum Sm,n = [summation operator]m+nk=m+1Xk, where m [greater-or-equal, slanted] 0 and n [greater-or-equal, slanted] 1. Further, let the function [varrho](n) = supm [greater-or-equal, slanted] 0[short parallel](1/n)Sm,n[short parallel]rr satisfy [summation operator][infinity]n=1[varrho](n)/n ;[varrho](2k) + [summation operator]kj=1((1 + cr)/2r)j-1[varrho](2k-j)} [reverse not equivalent] vk = o(k-1) as k --> [infinity], where cr = 2r-1. We also prove that for m [greater-or-equal, slanted] 0, p [greater-or-equal, slanted] 1, and [var epsilon] > 0, >P } pn [greater-or-equal, slanted] 2p((1/n)Sm,n) > [var epsilon]} [less-than-or-equals, slant] (2/[var epsilon]r)[summation operator][infinity]k=pvk --> 0 as p --> [infinity].

Keywords: Convergence; rate; cr-inequality; weakly; dependent; sequence (search for similar items in EconPapers)
Date: 1993
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