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不平衡单因素随机效应模型的区间估计AI 解读

Interval estimation of variance components is studied for the unbalanced one-way random effects model. An easily calculated function, $W$, of the harmonic mean of the class sizes and of the sample variance of the class means is found to be important. The exact distribution of $W$ is found and is shown to be excellently approximated by a chi-square distribution. The random variable $W$ is used to construct interval estimates for (i) the between classes variance component and…

双向分类混合模型设计的最小充分统计量AI 解读

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y=X τ+Z β+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties…

双向分类混合模型设计的最小充分统计量AI 解读

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y=X τ+Z β+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties…