Asymptotic distributions of the MLE's and the LR test in the growth curve model with a serial covariance structure
type: Item
instance of: scholarly article
title: Asymptotic distributions of the MLE's and the LR test in the growth curve model with a serial covariance structure
zbMATH Open document ID: 0724.62020
published in: Hiroshima Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The model considered in this paper is given by \(Y=A\Xi B+E\), \(N\times p\), where the rows of E are iid as \(N_ p(\cdot,\Sigma)\) and the covariance matrix \(\Sigma\) of the errors has the special structure of \(\Sigma =\sigma^ 2G(\rho)=\sigma^ 2(\rho^{| i-j|})\). By applying the theory of asymptotic expansions, the authors obtained the terms of the order \(N^{-1/2}\) in the asymptotic expansions of the distributions of the MLE of the parameters \(\sigma^ 2\) and \(\rho\), and consequently that of \(\Xi\) as well as the LR test.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62H15
zbMATH DE Number: 4194923
zbMATH Keywords: growth curve model
zbMATH Keywords: serial covariance structure
zbMATH Keywords: generalized multivariate analysis of variance
zbMATH Keywords: GMANOVA
zbMATH Keywords: likelihood ration test
zbMATH Keywords: linear models
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: multivariate analysis of variance
zbMATH Keywords: MANOVA
zbMATH Keywords: asymptotic expansions
author: Takashi Kanda
author: Yasunori Fujikoshi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206129180
OpenAlex ID: W1533856199
DOI: 10.32917/HMJ/1206129180
description: scientific article; zbMATH DE number 4194923