Estimation and testing in constrained covariance component models

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.