论文标题
与量身定制的极端特性的相关性
Correlations with tailored extremal properties
论文作者
论文摘要
最近，Chatterjee引入了一种新的相关系数，该系数具有多种自然属性。特别是，当一个变量是另一个变量的可测量函数时，系数才能达到其最大值。在本文中，我们试图定义具有相似属性的相关性，但现在可测量的函数必须属于预先指定的类，这等于对函数的形状限制。然后，我们将专门研究对应于单调非抵押函数类别的相关性，在这种情况下，我们可以证明各种渐近结果，并执行局部功率计算。
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable. In this paper, we seek to define correlations which have a similar property, except now the measurable function must belong to a pre-specified class, which amounts to a shape restriction on the function. We will then look specifically at the correlation corresponding to the class of monotone nondecreasing functions, in which case we can prove various asymptotic results, as well as perform local power calculations.
