Bernoulli

  • Bernoulli
  • Volume 14, Number 2 (2008), 301-321.

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

Tsung-Lin Cheng and Hwai-Chung Ho

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Abstract

Let Xn=∑i=1aiɛni, where the ɛi are i.i.d. with mean 0 and at least finite second moment, and the ai are assumed to satisfy |ai|=O(iβ) 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 ${\mathcal{R}}^{d+1}$ to $\mathcal{R}$, 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 $Q_{N}/\sqrt{N}$, QN=∑Nn=1(K(Xn, …, Xn+d)−EK(Xn, …, Xn+d)) are obtained when $Q_{N}/\sqrt{N}$ obeys the central limit theorem with positive limiting variance.

Article information

Source
Bernoulli Volume 14, Number 2 (2008), 301-321.

Dates
First available in Project Euclid: 22 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1208872106

Digital Object Identifier
doi:10.3150/07-BEJ112

Mathematical Reviews number (MathSciNet)
MR2544089

Zentralblatt MATH identifier
1155.62064

Keywords
Berry–Esseen bounds linear processes long memory long-range dependence non-instantaneous filters rate of convergence

Citation

Cheng, Tsung-Lin; Ho, Hwai-Chung. On Berry–Esseen bounds for non-instantaneous filters of linear processes. Bernoulli 14 (2008), no. 2, 301--321. doi:10.3150/07-BEJ112. https://projecteuclid.org/euclid.bj/1208872106.


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