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-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.
| Original language | English |
|---|---|
| Pages (from-to) | 301-321 |
| Number of pages | 21 |
| Journal | Bernoulli |
| Volume | 14 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2008 May 1 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
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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 journal › Article
TY - JOUR
T1 - On Berry-Esseen bounds for non-instantaneous filters of linear processes
AU - Cheng, Tsung L.
AU - Ho, Hwai Chung
PY - 2008/5/1
Y1 - 2008/5/1
N2 - 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.
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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U2 - 10.3150/07-BEJ112
DO - 10.3150/07-BEJ112
M3 - Article
VL - 14
SP - 301
EP - 321
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 2
ER -