The Annals of Statistics

Multivariate tests based on left-spherically distributed linear scores

Ekkehard Glimm, Siegfried Kropf, and Jürgen Läuter

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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.

Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1972-1988.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691365

Digital Object Identifier
doi:10.1214/aos/1024691365

Mathematical Reviews number (MathSciNet)
MR1673286

Zentralblatt MATH identifier
0929.62064

Subjects
Primary: 62F35: Robustness and adaptive procedures 62H15 62H20 62H25: Factor analysis and principal components; correspondence analysis 62J10 62J15: Paired and multiple comparisons

Keywords
Multivariate test linear scores spherical distribution generalized multivariate analysis exact test null robustness

Citation

Läuter, Jürgen; Glimm, Ekkehard; Kropf, Siegfried. Multivariate tests based on left-spherically distributed linear scores. Ann. Statist. 26 (1998), no. 5, 1972--1988. doi:10.1214/aos/1024691365. https://projecteuclid.org/euclid.aos/1024691365


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