
Accession Number : AD0668151
Title : ON TESTING A SET OF CORRELATION COEFFICIENTS FOR EQUALITY. I. SOME ASYMPTOTIC RESULTS.
Descriptive Note : Technical rept.,
Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
Personal Author(s) : Gleser,Leon Jay
Report Date : NOV 1967
Pagination or Media Count : 15
Abstract : Consider a random pdimensional vector x having a multivariate normal distribution. We are interested in testing the hypothesis H that the correlations rho sub ij between the elements of x are equal to a common value rho (i not = j). The likelihood ratio test of H versus general alternatives is difficult to evaluate and complicated in form. Alternative tests have been proposed by Bartlett (J.R.S.S. Ser. B 16 296298) by Lawley (Ann. Math. Statist. 34 149151), and by Aitkin and Nelson (unpublished). The asymptotic null distributions of Bartlett's and Lawley's tests have been obtained by Anderson (Ann. Math. Statist. 34 122148) and Lawley (loc. cit.). The asymptotic null distribution of the AitkinNelson test has not yet been obtained. The present paper obtains the asymptotic null distribution of the previously mentioned tests in a unified general fashion. Each of the above three tests is shown to be (under H) asymptotically equivalent to a member of a certain class of quadratic forms involving the sample correlations r sub ij. The asymptotic null distributions of such quadratic forms are obtained using the method of Lawley (loc. cit.). The null distribution of the AitkinNelson test is found to be dependent upon rho (the parameter unspecified in the null hypothesis) in such a fashion as to suggest that the AitkinNelson test is unpractical for most applications. (Author)
Descriptors : (*STATISTICAL ANALYSIS, THEOREMS), MATRICES(MATHEMATICS), STATISTICAL TESTS, STATISTICAL DISTRIBUTIONS, CORRELATION TECHNIQUES, SAMPLING, ANALYSIS OF VARIANCE, FUNCTIONS(MATHEMATICS)
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE