Estimation in a growth curve model with singular covariance

Let Y be a multivariate normal random matrix with covariance A circle times Sigma and mean mu is an element of S1S2' where S-i = {X(i)b(i) : K-i'b(i) = M-i'u(i) for some u(i)} and S1S2' is the linear span of the set of all x(1)x(2)' with x(i) is an element of S-i. Explicit formulae are obtained for the estimators of (mu,Sigma). These estimators are investigated through a large class of loss functions and other principles. None of the matrices A, Sigma, X-i, K-i and M-i are assumed to have full column rank. For robust studies, elliptical Y is considered when it is appropriate, (C) 2001 Elsevier Science B.V. All rights reserved.