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October 1998 Multivariate tests based on left-spherically distributed linear scores
Ekkehard Glimm, Siegfried Kropf, Jürgen Läuter
Ann. Statist. 26(5): 1972-1988 (October 1998). DOI: 10.1214/aos/1024691365

Abstract

In this paper, a method for multivariate testing based on low-dimensional, data-dependent, linear scores is proposed. The new approach reduces the dimensionality of observations and increases the stability of the solutions. The method is reliable, even if there are many redundant variables. As a key feature, the score coefficients are chosen such that a left-spherical distribution of the scores is reached under the null hypothesis. Therefore, well-known tests become applicable in high-dimensional situations, too. The presented strategy is an alternative to least squares and maximum likelihood approaches. In a natural way, standard problems of multivariate analysis thus induce the occurrence of left-spherical, nonnormal distributions. Hence, new fields of application are opened up to the generalized multivariate analysis. The proposed methodology is not restricted to normally distributed data, but can also be extended to any left-spherically distributed observations.

Citation

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Ekkehard Glimm. Siegfried Kropf. Jürgen Läuter. "Multivariate tests based on left-spherically distributed linear scores." Ann. Statist. 26 (5) 1972 - 1988, October 1998. https://doi.org/10.1214/aos/1024691365

Information

Published: October 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62064
MathSciNet: MR1673286
Digital Object Identifier: 10.1214/aos/1024691365

Subjects:
Primary: 62F35, 62H15, 62H20, 62H25, 62J10, 62J15

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 5 • October 1998
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