MINQE(U,I) AND UMVIQUE OF THE COVARIANCE-MATRIX IN THE GROWTH CURVE MODEL

Consider a general Growth Curve Model as follows Y = X1BX'(2) + UE, wh ere X(1),X(2), U(not equal 0) are known n x k, p x l, n x s matrices r espectively, B is an unknown k x l matrix of regression coefficients, Y = (y((1)),....,y((n)))' and E = (epsilon((1)),....,epsilon((s)))' ar e n x p matrix of observations and s x p matrix of random errors respe ctively, such that epsilon((1)),....,epsilon((s)) are independent rand om vectors with E epsilon((i)) = 0, E epsilon((i))epsilon((i)) = Sigma ,E(epsilon((i))epsilon((i))x epsilon((i))epsilon((i))) = Psi (it's exi stent and finite) i = 1,...,s, where Sigma and Psi are matrices of unk nown parameters. In the section 2 of this paper, for any given p x p m atrix C = C' not equal 0, we give the MINQE(U,I) of an estimable param eter function tr (C Sigma). Section 3 gives the n.s. conditions for tr (C Sigma)'s MINQE(U,I) to be a UMVIQUE. Section 4 gives the n.s, condi tions for tr(C Sigma)'s UMVIQUE to exist, and shows the MINQE(U,I) of tr (C Sigma) is just the UMVIQUE of tr (C Sigma) provided a UMVIQUE ex ists.