On Berry-Esseen bounds for non-instantaneous filters of linear processes

Tsung Lin Cheng, Hwai Chung Ho

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2 Citations (Scopus)

Abstract

Let Xn = Σi∞=1 aiε n-i, where the εi are i.i.d, with mean 0 and at least finite second moment, and the ai are assumed to satisfy ai = O(i) with β > 1/2. When 1/2 < β < 1, Xn is usually called a long-range dependent or long-memory process. For a certain class of Borel functions K(x1,..., xd+1), d ≥0, from Rd+1 to R, which includes indicator functions and polynomials, the stationary sequence K (Xn, Xn+1,..., Xn+d) is considered. By developing a finite orthogonal expansion of K (Xn,..., Xn+d), the Berry-Esseen type bounds for the normalized sum QN/√N, QN = ε nN=1 (K(Xn,..., Xn+d) - EK(Xn,..., Xn+d)) are obtained when QN/√N obeys the central limit theorem with positive limiting variance.

Original languageEnglish
Pages (from-to)301-321
Number of pages21
JournalBernoulli
Volume14
Issue number2
DOIs
Publication statusPublished - 2008 May 1

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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