INADMISSIBILITY AND ADMISSIBILITY RESULTS FOR UNBIASED

Let Y be distributed according to an n-variate normal distribution with a mean X~ and a nonsingular covariance matrix cr2V ", where both X and V are known, ]~ E R p is a parameter, o" ~> 0 is known or unknown. Denote ]~ = (X'V-IX) - X'V-IY and S 2 = (Y - X~)'V-I(Y - X]~). Assume that F~ is linearly estimable. When o" is known, it is proved that the unbiased loss estimator ¢y2tr(F(X'V-IX)- F') of (F~ - F~)'(F~ - F~) is admissible for rank (F) = ]c _~ 4 and inadmissible for ]c > 5 with the squared error loss [a-- (F~ - F~)'(F~ -F~)I 2. When o" is unknown and rank (X} 5 with squared error loss.