Asymptotic expansions for perturbed systems on Wiener space: Maximum likelihood estimators
type: Item
instance of: scholarly article
title: Asymptotic expansions for perturbed systems on Wiener space: Maximum likelihood estimators
zbMATH Open document ID: 0845.62054
author: Nakahiro Yoshida
published in: Journal of Multivariate Analysis
publication date: 1996-09-18T00:00:00Z
review text: We consider stochastic systems with unknown parameters disturbed by white Gaussian noises or normal random variables. For many such systems the unknown parameters can be estimated consistently by certain statistical estimators when the disturbances become small and the stochastic system tends to the corresponding deterministic one. For instance, the maximum likelihood method and the Bayes method are available for diffusion processes with unknown parameters in their drifts when the diffusion coefficient is small. In this case, the maximum likelihood estimator and the Bayes estimator are consistent and efficient in the first order. As for higher order properties of estimators, they are known to be second-order efficient in a certain sense. This fact follows from their asymptotic expansions in consideration of a problem of hypothesis testing. Thus asymptotic expansions for estimators play an important role in higher order statistical inference. The purpose of this article is to derive asymptotic expansions for likelihood ratio statistics and maximum likelihood estimators of unknown parameters involved in a system slightly disturbed by white Gaussian noises or normal random variables.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 889777
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: second order asymptotic efficiency
zbMATH Keywords: white Gaussian noises
zbMATH Keywords: normal random variables
zbMATH Keywords: disturbances
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: likelihood ratio statistics
zbMATH Keywords: maximum likelihood estimators
MaRDI profile type: Publication
OpenAlex ID: W2014032049
DOI: 10.1006/JMVA.1996.0019
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description: scientific article; zbMATH DE number 889777