Rank correlation is invariant to bijective marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation for continuous variables developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

中文翻译：

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分类混杂下的排名相关性

等级相关对于双射边际变换是不变的，但它也不能避免混杂。假设观察到分类混杂变量，作者提出了在基于 copula 的更大框架内开发的连续变量的加权相关系数。虽然在混杂因素暗示的每个组内的依赖性相同的假设下，权重是明确的，但作者扩展了最小平均均方误差 (MAMSE) 权重，以在各个组之间的依赖性可能有所不同时借用组之间的力量。推导了所提出系数的渐近特性，并使用模拟来评估其有限样本特性。