Estimation and testing in constrained covariance component models
By FRANK H. SHAW
Department of Ecology, Evolution and Behavior
University of Minnesota, St. Paul, Minnesota, 55108, U. S. A.
and CHARLES J. GEYER
School of Statistics
University of Minnesota, Minneapolis, Minnesota, 55455, U. S. A.
Abstract
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
semi-definite. 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.