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April 1999 Asymptotic Distribution of Quadratic Forms
F. Götze, A. N. Tikhomirov
Ann. Probab. 27(2): 1072-1098 (April 1999). DOI: 10.1214/aop/1022677395

Abstract

We consider quadratic forms $$Q_n = \sum_{1 \le j \neq k \le n} a_{jk}X_j X_k,$$ where $X_j$ are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of $Q_n$ and the distribution of the same quadratic forms with $X_j$ replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well as to nonstationary AR(1) processes.

Citation

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F. Götze. A. N. Tikhomirov. "Asymptotic Distribution of Quadratic Forms." Ann. Probab. 27 (2) 1072 - 1098, April 1999. https://doi.org/10.1214/aop/1022677395

Information

Published: April 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0941.60049
MathSciNet: MR1699003
Digital Object Identifier: 10.1214/aop/1022677395

Subjects:
Primary: 60F05

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 1999
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