Spherical Matrix Distributions and a Multivariate Model

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1977 · Volume 39 · Issue 2

DOI: 10.1111/j.2517-6161.1977.tb01623.x

Abstract

We consider inference about the parameters of a multivariate linear model, in which the usual assumption of normality for the errors is replaced by a weaker assumption of spherical symmetry. Structural distributions and confidence regions are derived, and it is shown that inference about means is identical with that appropriate under normality, being based on a matrix generalization of “Studentization”. Some relevant distribution theory is developed, the approach throughout being “density-free”.

Keywords

random matrix, spherical distribution, density-free methods, “studentization”, matric-variatetdistribution, structural inference, confidence regions

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