
Accession Number : AD0675599
Title : INFERENCE IN MULTIVARIATE NORMAL POPULATIONS WITH STRUCTURE. PART 1: INFERENCE ON VARIANCE WHEN CORRELATIONS ARE KNOWN.
Descriptive Note : Technical rept. no. 1,
Corporate Author : MINNESOTA UNIV MINNEAPOLIS
Personal Author(s) : Styan,George P. H.
Report Date : 09 AUG 1968
Pagination or Media Count : 85
Abstract : In this paper the case in which the correlations are known but the variances and means are all unknown is studied. Use is made of matrix algebra, employing the notion of Hadamard (or Schur) product of matrices, which is believed to be an innovation in statistical analysis, apart from a brief mention by Srivastava (1967). The variances are estimated by the method of maximum likelihood and a closed form is obtained for the resulting equations. These constitute a set of simultaneous nonhomogeneous quadratic equations which in general cannot be solved analytically. It is shown that they have a unique real solution; an approximation to this by the NewtonRaphson technique is obtained. (Author)
Descriptors : (*MULTIVARIATE ANALYSIS, CORRELATION TECHNIQUES), NUMERICAL METHODS AND PROCEDURES, MATRICES(MATHEMATICS), POPULATION(MATHEMATICS), APPROXIMATION(MATHEMATICS), SIMULTANEOUS EQUATIONS, SAMPLING, STATISTICAL TESTS, COMPUTER PROGRAMS, DECISION THEORY, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE