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对 Conway–Roberts 文章的若干观察、建议与评论AI 解读

This comment has two purposes. First, it will be shown that in two common situations, whenever one has unfairness 1 (using Conway and Roberts's terminology) against females and unfairness against males simultaneously, it is a mathematical necessity that males must have been in a position that was unfair in sense 2 (to use Conway and Roberts's phrase) at the outset. This mathematical result leads to an interesting question of semantics. Second, we will suggest an alternate…

平衡混合方差分析模型中的显式最大似然估计AI 解读

A result of Szatrowski, giving necessary and sufficient conditions for the existence of explicit maximum likelihood estimates for multivariate normal means and covariances with linear structure, can be applied to the problem of obtaining explicit maximum likelihood estimates in the mixed model of the analysis of variance. This application yields a simple procedure for checking whether or not explicit maximum likelihood estimates exist for the parameters in the balanced mixed…

方差分析混合模型中最大似然估计的渐近性质AI 解读

We show that in the mixed model of the analysis of variance, there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal, and efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix. These results follow directly by an application of a general result of Weiss (1971, 1973) concerning maximum likelihood estimates. This problem differs from standard problems in that we do not have independent, identically…