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Sharp large deviations for Gaussian quadratic forms with applications

Published online by Cambridge University Press:  15 August 2002

Bernard Bercu ,
Fabrice Gamboa  and
Marc Lavielle
Bernard Bercu
Affiliation:
Université Paris-Sud, bâtiment 425, 91405 Orsay Cedex, France; Bernard.Bercu@math.u-psud.fr.
Fabrice Gamboa
Affiliation:
Université Paul Sabatier, Toulouse, France; Gamboa@cict.fr.
Marc Lavielle
Affiliation:
Université René Descartes and Université Paris-Sud, France; Marc.Lavielle@math.u-psud.fr.
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Abstract

Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical spectral repartition function.

Keywords

Large deviationsGaussian processesquadratic formsToeplitz matrices.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 4 , 2000 , pp. 1 - 24
Copyright
© EDP Sciences, SMAI, 2000

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