Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model
type: Item
instance of: scholarly article
title: Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model
zbMATH Open document ID: 0637.62018
DOI: 10.1007/BF02491456
author: Yasunori Fujikoshi
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: For a generalized MANOVA model \(Y=A\Xi B+\epsilon\), where Y is an \(N\times p\) matrix, A is a known \(N\times k\) matrix of rank \(k\leq N\), B is a known \(q\times p\) matrix of rank \(q\leq p\) and \(\Xi\) is a \(p\times q\) matrix of unknown parameters, \(\epsilon\) is an \(N\times p\) disturbance matrix whose rows have independent p-variate normal distribution with unknown covariance matrix \(\Sigma\). Denote by \({\hat \Xi}\) the MLE of \(\Xi\). The author considers the distributions of \[ {\hat \Theta}=(A'A)^{1/2}({\hat \Xi}-\Xi)(B\Sigma^{-1}B')^{1/2}\quad and\quad {\hat \theta}=a'({\hat \Xi}-\Xi)b/\sigma \] where \(a=(a_ 1,...,a_ k)'\), \(b=(b_ 1,...,b_ g)'\) are fixed vectors and \(\sigma\) \(2=a'(A'A)^{-1}ab'(B\Sigma^{-1}B')^{-1}b\). Asymptotic expansions of the distribution function and of the density function of \({\hat \theta}\) and error bounds for these expansions are obtained. The results on the density function of \({\hat \theta}\) are generalized for the density function of the matrix variates \({\hat \Theta}\).
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 4039004
zbMATH Keywords: maximum likelihood estimators
zbMATH Keywords: MLE
zbMATH Keywords: GMANOVA model
zbMATH Keywords: generalized MANOVA model
zbMATH Keywords: Asymptotic expansions
zbMATH Keywords: error bounds
MaRDI profile type: Publication
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cites work: Q5519244
cites work: Q5512461
cites work: An error bound for an asymptotic expansion of the distribution function of an estimate in a multivariate linear model
cites work: Q5667383
cites work: Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
cites work: A method for approximations to the PDF's and CDF's of GLSE's and its application to the seemingly unrelated regression model
cites work: On Certain Distribution Problems Based on Positive Definite Quadratic Functions in Normal Vectors
cites work: A generalized multivariate analysis of variance model useful especially for growth curve problems
description: scientific article; zbMATH DE number 4039004