MANOVA模型中均值参数的极大极小估计和可容许估计

Abstract

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

CLC Number:

62C15

CHEN Qing-Ping, LI Na-Na, XIAO Zhi-Hong. Minimax Estimation and Admissible Estimation Under Normal MANOVA Model[J].Acta mathematica scientia,Series A, 2005, 25(4): 577-583.

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Minimax Estimation and Admissible Estimation Under Normal MANOVA Model

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