
Accession Number : ADA115377
Title : On Tests for Equicorrelation Coefficient and the Generalized Variance of a Standard Symmetric Multivariate Normal Distribution.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CA DEPT OF STATISTICS
Personal Author(s) : Gupta,Ashis Sen
PDF Url : ADA115377
Report Date : May 1982
Pagination or Media Count : 28
Abstract : It is observed that the standard multivariate normal distribution with equicorrelation coefficient, say rho, plays an important role in applied sciences. Tests for rho are derived. The likelihood ratio test is computationally cumbersome, vacuous against onesided alternatives with positive probability and the exact distribution of the test statistic is nearly intractable. Alternatively, a test based on the best 'natural' unbiased estimator of rho is proposed. It turns out to be locally most powerful and globally unbiased against onesided alternatives. The exact null and nonnull distributions of the test statistic which are of historical interest are derived and the exact percentage points are available. Large sample approximations are also given. With constrained parameter space, a simple test for rho based on the eigenvalues of the sample correlation matrix is proposed. The null and nonnull asymptotic distributions of the corresponding test statistics are given and the unbiasedness of the test is studies. Finally, we present the likelihood ratio test and a simple test based on the eigenvalues of the sample correlation matrix as tests for the generalized variance after establishing that they can be characterized through tests for rho. (Author)
Descriptors : *Normal distribution, *Multivariate analysis, Functions(Mathematics), Symmetry, Coefficients, Test methods, Eigenvalues, Matrices(Mathematics), Asymptotic normality, Vector analysis, Random variables, Correlation techniques
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE