Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes
type: Item
instance of: scholarly article
title: Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes
zbMATH Open document ID: 0595.62091
DOI: 10.1016/0047-259X(86)90055-2
author: Masanobu Taniguchi
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: The k-th order asymptotic efficiency is defined by the highest probability concentration around the true value by the k-th order Edgeworth expansion. The evaluation of various third-order asymptotic properties of MLE's for Gaussian ARMA processes is based on asymptotic moments of some statistics corresponding to the first three derivatives of the likelihood. The author proves that even in smooth cases the MLE is not always asymptotically efficient in the class \(A_ 3\) of third-order asymptotically median unbiased estimators. However, an appropriately modified MLE is always third-order asymptotically efficient in a subclass \(D\subset A_ 3\).
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3958503
zbMATH Keywords: Gaussian autoregressive moving average processes
zbMATH Keywords: spectral density
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: maximum likelihood estimator
zbMATH Keywords: residue theorem
zbMATH Keywords: asymptotic efficiency
zbMATH Keywords: highest probability concentration
zbMATH Keywords: Edgeworth expansion
zbMATH Keywords: Gaussian ARMA processes
zbMATH Keywords: asymptotically median unbiased estimators
reviewed by: Jiří Anděl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3958503