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On Testing Hypotheses Regarding a Class of Covariance Structures

Published online by Cambridge University Press:  01 January 2025

J. N. Srivastava
J. N. Srivastava*
Affiliation:
University of Nebraska
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Abstract

Let x be a p-component random variable having a multivariate normal distribution with covariance matrix Σ. In this paper, we consider the problem of testing hypotheses of the form H0:Σ = b1Σ1 + … + bmΣm, where bi's are unknown scalars, and Σi's are a set of known and simultaneously diagonalizable matrices. This problem has both psychometric and statistical interest, and its basic theory is developed here. Besides, the problem of obtaining likelihood-ratio statistic for testing H0 is studied, and the statistic obtained in a special case.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 2 , June 1966 , pp. 147 - 164
Copyright
Copyright © 1966 Psychometric Society

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