INFERENCE IN MULTIVARIATE NORMAL POPULATIONS WITH STRUCTURE. PART 1: INFERENCE ON VARIANCE WHEN CORRELATIONS ARE KNOWN.

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 Newton-Raphson technique is obtained. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 09, 1968
Accession Number
AD0675599

Entities

People

  • George P. H. Styan

Organizations

  • University of Minnesota

Tags

DTIC Thesaurus Topics

  • Algebra
  • Computing-Related Activities
  • Cooperation
  • Data Science
  • Differential Equations
  • Equations
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematics
  • New York
  • Quadratic Equations
  • Regression Analysis
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms