Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We study nonparametric estimators of such quantities using kernel smoothing techniques. Then, we assume a regression-type relationship between conditional Kendall's tau and covariates, in a parametric setting with possibly a large number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion. The theoretical properties of all these estimators are stated. We prove non-asymptotic bounds with explicit constants that hold with high probability. We derive their consistency, their asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.

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关于 Kendall 的回归

条件 Kendall 的 tau 是两个随机变量之间依赖关系的度量，条件是某些协变量。我们使用核平滑技术研究此类数量的非参数估计量。然后，我们假设条件 Kendall's tau 和协变量之间存在回归类型的关系，在可能有大量回归变量的参数设置中。这个模型可能是稀疏的，底层参数是通过惩罚标准估计的。说明了所有这些估计量的理论特性。我们证明了具有高概率的显式常数的非渐近边界。我们推导出它们的一致性、它们的渐近律和一些预言机属性。对真实数据的一些模拟和应用总结了本文。