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**Example text**

2. fe trCBi--fi}. 3) @YUDis not empty iff convex span {q(b): b~R"} where q(b) = ( b ' M V I M b ..... b'MVpMb)'. 5) where q(b) = (b'Blb ..... b'Bpb). 5) are rather complicated, but simple results can be obtained if we assume V1..... d. 1. Let V//> 0 , i = 1..... p, V=Y, V,. 2). 6) where R ( . ) denotes the rank of a matrix. 7) where G is the projection operator onto the space generated by the columns of the compound matrix (g: VI:... : 5-1; 5+1:"" : Vp). 1 shows that at most 01 is nonnegatively estimable.

9). t0) becomes trDV~A,V~>O V D ~ @ , ® = ( D : D X = O , A , + O ~>O,trDV/--O,i--- 1..... p}. 11) cannot be explicitly written down, but the formula will be useful in examining whether any guessed solution for A , provides a MINQE(U, NND). We shall consider some special cases. 2. Let V//> 0, i = 1..... 9) is satisfied. 13) where G is the projection operator onto the space generated by the columns of ( X , V 1. . . Vj_I, Vj+ 1. . , Vp). 9) based on standard methods of convex programming is provided by Pukelsheim (1977, 1978a, b).

10 The hypothesis is rejected at the a = 0 . 12 so that H 0 is rejected. ). In the analysis of the one-group repeated measurements design from a multivariate analysis of variance point of view, no restrictions were placed on the structure of the variance-covariance matrix Z (except that n >p to ensure a positive definite estimate). If, however, mixed model univariate assumptions are established for a set of data, a univariate analysis is readily obtained from a set of multivariate calculations provided the post matrix A is orthogonalized so that A'A = I.