A Copula‐Based Non‐parametric Measure of Regression Dependence

A Copula‐Based Non‐parametric Measure of Regression Dependence
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基于 Copula 的回归依赖性非参数测量

DOI：
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发表时间：
2013
期刊：
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通讯作者：
Pavel A. Stoimenov
Pavel A. Stoimenov
中科院分区：
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文献类型：
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作者：
H. Dette;K. Siburg;Pavel A. Stoimenov

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摘要。本文提出了一个根据回归依赖程度比较二元分布的框架。我们介绍了回归相关阶（RDO）的一般概念。此外，我们定义了一种新的回归相关的非参数测度，并研究了它的性质。除了在新的rdo中是单调的之外，该度量分别在独立和几乎确定的函数依赖处取极值。构造了新测度的一致非参数估计量，并研究了其渐近性质。最后，通过小型仿真研究，研究了估计的有限样本性质。
Abstract.  This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.