Asymptotic expansion for the distribution of the discriminant function in the first order autoregressive processes
type: Item
instance of: scholarly article
title: Asymptotic expansion for the distribution of the discriminant function in the first order autoregressive processes
zbMATH Open document ID: 0615.62075
author: Hirofumi Wakaki
author: Ho-Se Oh
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: This paper is concerned with the problem of classifying a series of T observations coming from one of two first order autoregressive Gaussian processes. The processes are determined by the stochastic equations \(y_ t=\alpha_ jy_{t-1}+u_ t\) \((t=...-1,0,1,...)\) where \(\alpha_ j\) \((| \alpha_ j| <1)\) is known, and \(u_ t's\) are independent identically distributed as \(N(0,\sigma^ 2_ j)\) with known variance \(\sigma^ 2_ j\) \((j=1,2)\). We consider the discriminant function based on the Bayes method, which is a quadratic function of observations. We derive an asymptotic expansion of the distributions of the discriminant function and give an approximation for the probabilities of misclassifications.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3996902
zbMATH Keywords: classification
zbMATH Keywords: first order autoregressive Gaussian processes
zbMATH Keywords: discriminant function
zbMATH Keywords: Bayes method
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: probabilities of misclassifications
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3996902