MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE COVARIANCE COMPONENTS FOR THE BALANCED ONE-WAY LAYOUT.
Abstract
Unbiased estimators of variance and covariance components for the balanced one-way layout have been extensively investigated in the literature. Unfortunately, they possess the unpleasant property of taking on inadmissible values such as negative variances and, more generally, non-positive-semidefinite covariance matrices. This in turn can lead to correlation coefficients that are imaginary or greater than one. In the univariate case, the maximum likelihood (m. l.) estimators, which are free from these drawbacks, have been derived by Herbach and shown elsewhere to have uniformly, and in many cases considerably, smaller mean square errors than the unbiased estimators. Hence it is of interest to consider m. l. estimation in the multivariate case. Searle computed the information matrix for the bivariate case, but did not derive explicit expressions for the estimators. In this paper, the maximum likelihood estimators for the general P-variate case are derived. The methods of computation are described, and explicit formulae are given for the bivariate case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1968
- Accession Number
- AD0681035
Entities
People
- Jerome Klotz
- Joseph Putter
Organizations
- University of Wisconsin–Madison