平衡数据结构下ANOVA估计和SD估计的比较

Comparison between ANOVA estimator and SD estimator under balanced data

在线性混合效应模型下,方差分析(ANOVA)估计和谱分解(SD)估计对构造精确检验和广义P-值枢轴量起着非常重要的作用.尽管这两估计分别基于不同的方法,但它们共享许多类似的优点,如无偏性和有精确的表达式等.本文借助于已得到的协方差阵的谱分解结果,揭示了平衡数据一般线性混合效应模型下ANOVA估计与SD估计的关系,并分别针对协方差阵两种结构:套结构和多项分类随机效应结构,给出了ANOVA估计与SD估计等价的充分必要条件.

The analysis of variance （ANOVA） estimator and the spectral decomposition （SD） estimator are very helpful for constructing exact test statistics and generalized P -value pivotal variables under linear mixed-effects models. Though two estimators are constructed with completely different methods, they share many similar advantages, such as unbiased and closed form. In this paper, we make some comparison between ANOVA estimator and SD estimator. Based the spectral decomposition of covariance matrix we have obtained, we discover the relationship between ANOVA estimator and SD estimator, and establish necessary and sufficient conditions for the identity of ANOVA estimator and SD estimator for the models with nest-structure covariance matrix and the models with multi-way crossed classification random effects, respectively.