GMANOVA-MANOVA模型中的两阶段抽样估计
Two-Stage Sampling Estimators in the GMANOVA-MANOVA Model
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摘要: 对于GMANOVA-MANOVA模型\left\\beginarraylY=X_1 B_1 X_2^\prime+Z B_2+\varepsilon, \\ \operatornameCov(Y)=\Sigma \otimes I_n .\endarray\right. 本文通过两阶段抽样构造出了其均值参数矩阵B1,B2的一种估计\widehatB_1 N_1, \widehatB_2 N_2,使得这种估计在二次损失下,其风险小于任意预先给定的ε>0,并且证明了这种估计的停时数(stop number)是渐近有效的(在Chow and Robbins(1965)意义下)。Abstract: For regression coefficient matrices of the GMANOVA-MANOVA model, this paper gives gives two- stage estimators, such that their risk functions related to arbitrary quadratic loss are bounded above a preassigned constant.Their asymptotic effciency are also discussed.