Inference in Multivariate Normal Populations with Structure. Part 1: Inference on Variance when Correlations Are Known

摘要

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 Newton-Raphson technique is obtained. (Author)