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February 1999 Limit theorems for quadratic forms with applications to Whittle's estimate
Lajos Horváth, Qi-Man Shao
Ann. Appl. Probab. 9(1): 146-187 (February 1999). DOI: 10.1214/aoap/1029962600

Abstract

We establish strong and weak approximations for quadratic forms of weakly and strongly dependent random variables and obtain necessary and sufficient conditions for the weak convergence of weighted functions of quadratic forms. The results are applied to get the asymptotic distributions of some tests which can be used to detect possible changes in the long-memory parameter.

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Lajos Horváth. Qi-Man Shao. "Limit theorems for quadratic forms with applications to Whittle's estimate." Ann. Appl. Probab. 9 (1) 146 - 187, February 1999. https://doi.org/10.1214/aoap/1029962600

Information

Published: February 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0940.60037
MathSciNet: MR1682588
Digital Object Identifier: 10.1214/aoap/1029962600

Subjects:
Primary: 60F03 , 60F17
Secondary: 60F15 , 60G70

Keywords: Change-point , limit theorems , linear process , long-memory parameter , Quadratic forms , Strong and weak approximations , weight functions

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.9 • No. 1 • February 1999
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