Let X1,...,X(N) (where N > m) be independent N(m)(mu, SIGMA) random vectors, and put [GRAPHICS] where T is upper-triangular with positive diagonal elements. The author considers the problem of estimating SIGMA, and restricts his attention to the class of estimates D = {T' DELTA*T + Nb* XBAR XBAR':DELTA* is any diagonal matrix and b* is any nonnegative constant} because it has the following attractive features: (a) Its elements are all quadratic forms of the sufficient and complete statistics (XBAR, T). (b) It contains all estimates of the form aA + NbXBARXBAR' (a greater-than-or-equal-to 0 and...
