INADMISSIBILITY AND ADMISSIBILITY RESULTS FOR UNBIASED LOSS ESTIMATORS BASED ON GAUSS-MARKOV ESTIMATORS

LetY be distributed according to ann-variate normal distribution with a meanXβ and a nonsingular covariance matrixσ2V, where bothX andV are known,β εR p is a parameter,σ > 0 is known or unknown. Denote\(\hat \beta = (X'V^{ - 1} X)^ - X'V^{ - 1} Y\) and\(S^2 = (Y - X\hat \beta )'V^{ - 1} (Y - X\hat \beta )\). Assume thatFβ is linearly estimable. Whenσ is known, it is proved that the unbiased loss estimatorσ2tr(F(X′V−1X)−F′) of\((F\hat \beta - F\beta )'(F\hat \beta - F\beta )\) is admissible for rank (F)=k≤4 and inadmissible fork ≥ 5 with the squared error loss\([a - (F\hat \beta - F\beta )'(F\hat \beta - F\beta )]^2\). Whenσ is unknown and rank (X) 更多