多元线性混合模型方差分量矩阵的非负估计

Nonnegative Estimation of Variance Component Matrix in Multivariate Linear Mixed Model

本文研究了带有两个方差分量矩阵的多元线性混合模型方差分量矩阵的估计问题.对于平衡模型,给出了基于谱分解估计的一个方差分量矩阵的非负估计类.对于非平衡模型,给出了方差分量矩阵的广义谱分解估计类,讨论了与ANOVA估计等价的充要条件.同时,在广义谱分解估计的基础上给出了一种非负估计类,并讨论了其优良性.当具有较小二次风险的非负估计不存在时,从估计为非负的概率的角度考虑,将Kelly和Mathew(1993)提出的构造具有更小取负值概率的估计类的方法推广到本文的多元模型下,给出了较谱分解估计相比有更小取负值概率和更小风险的估计类.最后,模拟研究和实例分析表明文中理论结果有很好的表现.

Multivariate linear mixed model with two variance components matrices is considered. For balanced model, based on spectral decomposition estimate （SDE）, a class of nonnegative estimate of variance components matrices is proposed. For unbalanced model, a so-called generalized spectral decomposition estimate （GSDE） of variance components matrices is obtained. Our results show a sufficient and necessary condition for the GSDE to be equal to the analysis of variance estimate （ANOVAE）. And then, based on GSDE, we also propose a class of nonnegative estimate and discuss the optimality. Furthermore, we extend the method proposed by Kelly and Mathew （1993） to multivariate model in this paper. Finally, some simulations and applications to illustrate the results are presented.