Higher-order asymptotic theory for discriminant analysis of Gaussian ARMA processes
type: Item
instance of: scholarly article
title: Higher-order asymptotic theory for discriminant analysis of Gaussian ARMA processes
zbMATH Open document ID: 0806.62049
DOI: 10.1016/0167-7152(94)90013-2
author: G. Zhang
published in: Statistics \& Probability Letters
publication date: 1995-02-16T00:00:00Z
review text: This paper develops a higher-order asymptotic theory for discriminant analysis in time series. Higher-order asymptotic analysis may be necessary if the sample size is not large. Two discriminant statistics for Gaussian autoregressive processes are given. Then the asymptotic approximations of misclassification probabilities are derived -- the second-order one for Gaussian ARMA processes and the third-order one for Gaussian AR(1) processes. A numerical simulation study for the Gaussian ARMA(1,1) process with small samples is performed using the above two discriminant statistics, and the results are both close to the theoretical detection probabilities of the log-likelihood ratio.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 633495
zbMATH Keywords: higher-order asymptotic theory
zbMATH Keywords: discriminant analysis
zbMATH Keywords: time series
zbMATH Keywords: Gaussian autoregressive processes
zbMATH Keywords: asymptotic approximations
zbMATH Keywords: misclassification probabilities
zbMATH Keywords: Gaussian ARMA processes
zbMATH Keywords: Gaussian AR(1) processes
zbMATH Keywords: numerical simulation study
zbMATH Keywords: log-likelihood ratio
reviewed by: V. Yu. Urbakh
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90013-2
OpenAlex ID: W2069430830
cites work: Q3947020
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cites work: Q3681765
cites work: Higher order asymptotic theory for time series analysis
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description: scientific article; zbMATH DE number 633495