Large deviations for quadratic forms of stationary Gaussian processes

[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.

[发布日期] 1997-10-30

[关键词] large deviations;quadratic forms;Gaussian processes;Toeplitz matrices