Estimation and testing in constrained covariance component models

Frank H. Shaw, Charles J. Geyer

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


A cutting plane algorithm is proposed for estimating variance and covariance components by maximum likelihood or restricted maximum likelihood enforcing the constraints that covariance matrices be positive semidefinite. For tests of hypotheses involving these constrained estimates, an asymptotic parametric bootstrap is proposed for approximating the distribution of the likelihood ratio test statistic. Although the bootstrap is generally inconsistent when the true parameter value is on the boundary of the feasible region, the double bootstrap can be used to show that the ordinary bootstrap works well in certain problems.

Original languageEnglish (US)
Pages (from-to)95-102
Number of pages8
Issue number1
StatePublished - Jan 1 1997


  • Asymptotic parametric bootstrap
  • Cutting plane algorithm
  • Semi-infinite programming
  • Variance component


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