The Annals of Applied Probability

Limit theorems for quadratic forms with applications to Whittle's estimate

Lajos Horváth and Qi-Man Shao

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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.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 1 (1999), 146-187.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962600

Digital Object Identifier
doi:10.1214/aoap/1029962600

Mathematical Reviews number (MathSciNet)
MR1682588

Zentralblatt MATH identifier
0940.60037

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60F03
Secondary: 60F15: Strong theorems 60G70: Extreme value theory; extremal processes

Keywords
Strong and weak approximations change-point quadratic forms limit theorems weight functions linear process long-memory parameter

Citation

Horváth, Lajos; Shao, Qi-Man. Limit theorems for quadratic forms with applications to Whittle's estimate. Ann. Appl. Probab. 9 (1999), no. 1, 146--187. doi:10.1214/aoap/1029962600. https://projecteuclid.org/euclid.aoap/1029962600


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