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

Tsung L. Cheng, Hwai Chung Ho

Research output: Contribution to journalArticle

1 Citation (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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Berry-Esseen Bound
Linear Process
Filter
Orthogonal Expansion
Long Memory Process
Borel Functions
Indicator function
Stationary Sequences
Central limit theorem
Limiting
Moment
Polynomial
Dependent
Range of data
Class

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Cheng, Tsung L. ; Ho, Hwai Chung. / On Berry-Esseen bounds for non-instantaneous filters of linear processes. In: Bernoulli. 2008 ; Vol. 14, No. 2. pp. 301-321.
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On Berry-Esseen bounds for non-instantaneous filters of linear processes. / Cheng, Tsung L.; Ho, Hwai Chung.

In: Bernoulli, Vol. 14, No. 2, 01.05.2008, p. 301-321.

Research output: Contribution to journalArticle

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AB - 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-β) 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.

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