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本文综述混合效应模型参数估计方面的若干新进展. 平衡混合效应方差分析模型的协方差阵具有一定结构. 对这类模型, 文献[1]提出了参数估计的一种新方法, 称为谱分解法. 新方法的突出特点是, 能同时给出固定效应和方差分量的估计, 前者是线性的, 后者是二次的,且相互独立. 而后, 文献[2--9]证明了谱分解估计的进一步的统计性质, 同时给出了协方差阵对应的估计, 它不仅是正定阵, 而且可获得它的风险函数, 这些文献还研究了谱分解估计与方差分析估计, 极大似然估计, 限制极大似然估计以及最小范数二次无偏估计的关系. 本文综述这一方向的部分研究成果, 并提出一些待进一步研究的问题.

On Spectral Decomposition Estimates in Mixed Linear Models

This paper gives a survey of the recent developments on parameter estimation in linear mixed model. The covariance matrix in balanced analysis of variance mixed linear models has a specific structure. For this model, [1] proposed a new approach, spectral decomposition method, to estimate parameters. The merits of the approach is to provide independent estimates of fixed effects and variance components simultaneously, the former is linear and late quadratic. [2--9] established some further properties of the new estimates and corresponding estimates of covariance matrix with risk function. These papers also obtained some relations among the analysis of variance estimate, maximum likelihood estimate, restricted maximum likelihood estimate, minimum norm quadratic unbiased estimate and new estimates. Finally, some open problems are proposed.