ESTIMATION AND TESTING IN CONSTRAINED COVARIANCE COMPONENT MODELS

A cutting plane algorithm is proposed for estimating variance and cova riance components by maximum likelihood or restricted maximum likeliho od enforcing the constraints that covariance matrices be positive semi definite. For tests of hypotheses involving these constrained estimate s, an asymptotic parametric bootstrap is proposed for approximating th e distribution of the likelihood ratio test statistic. Although-the bo otstrap 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.