关键词: 正态MANOVA模型, 极大极小估计, 可容许估计

Abstract:

Let random matrix Y_(n×m) be distributed according to N(XΘ, σ^2Σ×V),Where X is a known n×k matrix of rank k, n≥k≥3, σ^2 is unknown  and
σ^(-2)S_p has a χ square distribution with degree of freedom p. When f(t) is differentiable and f′(t)≥0,0≤f(t)≤2(k-2)/m(p+2), the estimator whose ithcolumn vector has the formΔ_i(Y)=[I_k- f(V′_iY′(X′Σ^(-1)X)^(-2)YV_iS_p_(-1)S_p (X′Σ^(-1)X)^(-1) /V′_iY′(X′Σ^(-1)X)^(-2)YV_i](X′Σ^(-1)X)^(-1)X′Σ^(-1)Y_i where V_i is the ith column vector of  V^(-1/2),can improve the maximum likelihood estimator (X′Σ^(-1)X)^(-1)X′Σ^(-1)Y of Θ. Moreover, some  classes  of admissible linear estimators for Θ or  CXΘ  are obta ined too

Key words: Normal MANOVA model, Minimax estimator, Admissible estimator