Abstract
The analysis of variance (ANOVA) estimator and the spectral decomposition (SD) estimator are very helpful for constructing exact test statistics and generalized <italic>P</italic>-value pivotal variables under linear mixedeffects 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.
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