Sharp large deviations for Gaussian quadratic forms with applications

Bernard Bercu; Fabrice Gamboa; Marc Lavielle

ESAIM: Probability and Statistics (2010)

  • Volume: 4, page 1-24
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Bercu, Bernard, Gamboa, Fabrice, and Lavielle, Marc. " Sharp large deviations for Gaussian quadratic forms with applications." ESAIM: Probability and Statistics 4 (2010): 1-24. <http://eudml.org/doc/116583>.

@article{Bercu2010,
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. },
author = {Bercu, Bernard, Gamboa, Fabrice, Lavielle, Marc},
journal = {ESAIM: Probability and Statistics},
keywords = {Large deviations; Gaussian processes; quadratic forms; Toeplitz matrices.; Toeplitz matrices},
language = {eng},
month = {3},
pages = {1-24},
publisher = {EDP Sciences},
title = { Sharp large deviations for Gaussian quadratic forms with applications},
url = {http://eudml.org/doc/116583},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Bercu, Bernard
AU - Gamboa, Fabrice
AU - Lavielle, Marc
TI - Sharp large deviations for Gaussian quadratic forms with applications
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 1
EP - 24
AB - 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.
LA - eng
KW - Large deviations; Gaussian processes; quadratic forms; Toeplitz matrices.; Toeplitz matrices
UR - http://eudml.org/doc/116583
ER -

References

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