Elliptical multivariate analysis
type: Item
instance of: scholarly article
title: Elliptical multivariate analysis
zbMATH Open document ID: 0669.62033
DOI: 10.1016/0304-4076(89)90093-6
author: Bernard M. S. van Praag
author: Bertram M. Wesselman
published in: Journal of Econometrics
publication date: 1989-01-01T00:00:00Z
review text: We investigate the interpretation and the asymptotic properties of the well-known statistics \({\hat \theta}\) derived in multivariate analysis, when the parent distribution of the observations is not necessarily normal but belongs to the wider class of elliptical distributions (including the normal). Our conclusion is that those statistics keep their geometric interpretation and consistency and that for most of those statistics the asymptotic distribution of \(\sqrt{T}({\hat \theta}- \theta)\) is \(N(0,(1+\kappa)var_ N)\), where \(var_ N\) is the covariance matrix under the normality assumption and where \(\kappa\) is the joint kurtosis parameter. For statistics of the \(\chi^ 2\)-type used in asymptotic test criteria, we find similar expressions. It follows that all multivariate software may be utilized in the elliptical context under the provision that \(\kappa\) is estimated in addition.
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4096589
zbMATH Keywords: distribution-free approach
zbMATH Keywords: asymptotic properties
zbMATH Keywords: elliptical distributions
zbMATH Keywords: consistency
MaRDI profile type: Publication
full work available at URL: 0304-4076(89)90093-6
OpenAlex ID: W2011187933
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description: scientific article; zbMATH DE number 4096589