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Sharp large deviations for Gaussian quadratic forms with applications. (English) Zbl 0939.60013

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 [R. R. Bahadur and R. R. Rao, Ann. Math. Stat. 31, 1015-1027 (1960; Zbl 0101.12603)] 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.

MSC:

60F10 Large deviations
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
11E25 Sums of squares and representations by other particular quadratic forms
60G15 Gaussian processes

Citations:

Zbl 0101.12603
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References:

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