Reml estimation of covariance matrices with restricted parameter spaces

James A. Calvin, Richard L. Dykstra

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Restricted parameter spaces for covariance matrices, such as ∑ = σ2I or ∑ = αI + βJ, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses. With multivariate variance components models, several covariance matrices need to be simultaneously estimated and, even with a reduced parameter space, estimation can be difficult. In earlier work we have discussed estimation for a widely-used class of models where the variance components matrices need only be nonnegative definite. In this article we extend these results to handle a wide class of restricted parameter spaces. We state the conditions required for a parameterization to be a member of the class, discuss the implementation of the results for several different members of the class, and discuss estimation with both balanced and unbalanced data. We give several examples to demonstrate the results.

Original languageEnglish (US)
Pages (from-to)321-329
Number of pages9
Issue number429
StatePublished - Mar 1995
Externally publishedYes


  • EM algorithm
  • Isotonic regression
  • Iterative algorithm
  • Multivariate linear model
  • Patterned matrices
  • Restricted maximum likelihood estimation
  • Variance components

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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