Large deviations for quadratic forms of stationary Gaussian processes

被引：76

作者：

Bercu, B

Gamboa, F

Rouault, A

机构：

[1] UNIV PARIS 13,INST GALILEE,F-93430 VILLETANEUSE,FRANCE

[2] UNIV VERSAILLES,DEPT MATH,F-78035 VERSAILLES,FRANCE

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1997年 / 71卷 / 01期

关键词：

large deviations; quadratic forms; Gaussian processes; Toeplitz matrices;

D O I：

10.1016/S0304-4149(97)00071-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A large deviation principle is proved for Toeplitz quadratic forms of centred stationary Gaussian processes. The rate function is obtained by a sharp study of the behaviour of eigenvalues of a product of two Toeplitz matrices. Some statistical applications such as the likelihood ratio test and the estimation of the parameter of an autoregressive Gaussian process are also provided. (C) 1997 Elsevier Science B.V.

引用

页码：75 / 90

页数：16

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[18]

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