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由二元函数加权和导出的置换统计量的渐近正态性AI 解读

Statistics of the form $H_n = \sum d_{ijn}h_n(X_i, X_j)$ are considered, where $X_1, X_2, \cdots$, are independent and identically distributed random variables, the diagonal terms, $d_{iin}$, are equal to zero, and $h_n(x, y)$ is a symmetric real valued function. The asymptotic normality of such statistics is proven and the result then combined with work of Jogdeo on statistics that are weighted sums of bivariate functions of ranks to find sufficient conditions for…

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最大似然成对比较排序与二次指派AI 解读

A connexion is identified between maximum likelihood paired-comparison ranking and the problem of quadratic assignment discussed in the operational research literature. This relationship immediately gives a set of computational techniques for obtaining the necessary rankings, and, in addition, provides a general framework for testing the reasonableness of particular object sequencings suggested a priori.