Some asymptotic inferential problems connected with complex elliptical distribution
type: Item
instance of: scholarly article
title: Some asymptotic inferential problems connected with complex elliptical distribution
zbMATH Open document ID: 0723.62016
DOI: 10.1016/0047-259X(90)90016-B
author: C. D. Bhavsar
author: Chinubal G. Khatri
published in: Journal of Multivariate Analysis
publication date: 1990-01-01T00:00:00Z
review text: The first author [ibid. 27, 319-333 (1988; Zbl 0659.62034)] proved an asymptotic normality of the location parameters of the generalized linear growth curve model when a set of independent observations are taken from an elliptical distribution and obtained an asymptotic confidence region on the location parameters, the asymptotic distribution of the canonical correlations and an asymptotic confidence region on the discriminatory value for the linear discriminant function. In this paper, the authors extend the above-mentioned results to complex elliptical variates. To write more precisely, let \(Z=(z_ 1,z_ 2,...,z_ n)\) be n independent observations on the complex vector and consider the linear growth curve model \(Z=B\xi A^*+\epsilon\), where \(\xi\) is an unknown parameter, A and B are complex matrices of full rank and \(\epsilon_ i\) are i.i.d. column vectors with complex elliptical distribution. The authors, among others, derive the asymptotic joint distribution of \[ Z A(A^*A)^{-1}\text{ and } n^{-1}(ZZ^*- ZA(A^*A)^{-1}\Lambda^*Z^*) \] and asymptotic confidence bounds on the elements of \(\xi\) when \(\Sigma =b_ 1^{-1}E \epsilon_ i\epsilon^*_ i\) is unknown.
reviewed by: Ken-ichi Yoshihara
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4192875
zbMATH Keywords: Fisher's linear discriminator
zbMATH Keywords: canonical correlations
zbMATH Keywords: discriminatory value
zbMATH Keywords: linear growth curve model
zbMATH Keywords: complex matrices of full rank
zbMATH Keywords: complex elliptical distribution
zbMATH Keywords: asymptotic joint distribution
zbMATH Keywords: asymptotic confidence bounds
MaRDI profile type: Publication
cites work: Q5842591
cites work: A note on a Manova model applied to problems in growth curve
cites work: Some asymptotic inferential problems connected with elliptical distributions
Recommended article: Some asymptotic inferential problems connected with elliptical distributions
Recommended article: Q3473948
Recommended article: Q3326634
Recommended article: Q4887142
Recommended article: Analysis of Covariance Structures Under Elliptical Distributions
Recommended article: Robustness study for a linear growth model
Recommended article: Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution
description: scientific article; zbMATH DE number 4192875