Least squares estimation of covariance matrices in balanced multivariate variance components models

James Arthur Calvin, Richard L. Dykstra

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative estimation procedure, satisfying a least squares criterion, that is guaranteed to produce nnd estimates of the covariance matrices, discuss the speed of convergence, and provide an example to show how the estimates change.

Original languageEnglish (US)
Pages (from-to)388-395
Number of pages8
JournalJournal of the American Statistical Association
Volume86
Issue number414
DOIs
StatePublished - Jan 1 1991

Keywords

  • Fenchel duality
  • Isotonic regression
  • Löwner ordering
  • Multivariate linear model
  • Nonnegative definite
  • Ordinary least squares
  • Unweighted least squares
  • Wishart density

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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