两个方差分量同时非齐次估计的可容许性

来源期刊：中南大学学报(自然科学版)1991年第1期

论文作者：王志忠

文章页码：104 - 110

关键词：方差; 统计模型; 容许性

Key words：variance; statistical model; admissibility

摘    要：考虑方差分量模型 E Y n×1=X n×p B p×1 DY=σ₁²V₁+σ₂²V₂ 其中β∈R^p,σ₁>0,σ₂>0均未知;X,V₁,V₂均已知。本文讨论方差分量(σ₁²,σ₂²)的估计在估计类D={d=(Y′AY+P′Y+f,Y′BY+q′Y+g):Y′AY+P′Y+f≥0,Y′BY+q′Y+g≥0,对一切Y}中的可容许性的问题。当X为满秩方阵时,给出了(σ₁²,σ₂²)的估计在D中可容许的充分条件和必要条件。

Abstract: Consider a variance-component model EY n×1=Xn×P βP×1 DY=σ₁²V₁+σ₂²V₂ where β∈R^p, σ₁>0, and σ₂>0, are all unknown, X, V₁, and V₂ arve all known. We discussed the problem about admissibility of the estimate of (σ₁², σ₂²)in the class D={d= (Y′AY+p′Y+f,Y′BY+q′ Y+g): Y′BY+q′Y+f≥0, Y′BY+q′Y+g≥0, for all γ's}. Here were offered both a sufficient condlition and a necessary condition of admissibility if rank (X_n×P)=n.