On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes
type: Item
instance of: scholarly article
title: On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes
zbMATH Open document ID: 0991.62061
DOI: 10.1016/S0304-4149(99)00063-0
author: Yoshihide Kakizawa
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: A spectral parameter of a mean zero Gaussian stationary process is estimated by maximum-likelihood (ML) and quasi-maximum-likelihood (qML) methods. It is shown that under some conditions the estimators are asymptotically efficient in the sense of Bahadur. A basic result of large deviation probability of a certain quadratic form is proved and by the help of it the exponential convergence rates of tail probabilities of these estimators are obtained. Efron's statistical curvature of Gaussian stationary processes is used in order to show the identity of the exponential convergence rates of the ML and qML estimators.
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 1792489
zbMATH Keywords: Bahadur efficiency
zbMATH Keywords: Gaussian stationary processes
zbMATH Keywords: spectral density
zbMATH Keywords: large deviation probabilities
zbMATH Keywords: Toeplitz matrix
MaRDI profile type: Publication
cites work: Q3845761
cites work: Q3736706
cites work: Large deviations for quadratic forms of stationary Gaussian processes
cites work: Time series: theory and methods.
cites work: Efficient parameter estimation for self-similar processes
cites work: Q5624436
cites work: Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
cites work: Central limit theorems for quadratic forms in random variables having long-range dependence
cites work: Large sample point estimation: A large deviation theory approach
cites work: Classical asymptotic properties of a certain estimator related to the maximum likelihood estimator
cites work: Q3752135
cites work: The asymptotic theory of linear time-series models
cites work: High-order efficiency in the estimation of linear processes
cites work: The second-order Fisher information
cites work: Q4003734
cites work: On exponential rates of estimators of the parameter in the first-order autoregressive process
cites work: Large Deviation Results for Statistics of Short‐ and Long‐memory Gaussian Processes
cites work: Higher order asymptotic theory for time series analysis
description: scientific article; zbMATH DE number 1792489