Correlations with tailored extremal properties
Preprint
Abstract
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.Keywords
All Related Versions
This publication has 10 references indexed in Scilit:
- A simple measure of conditional dependenceThe Annals of Statistics, 2021
- On the power of Chatterjee’s rank correlationBiometrika, 2021
- Distribution-free properties of isotonic regressionElectronic Journal of Statistics, 2019
- Chi-square approximation by Stein’s method with application to Pearson’s statisticThe Annals of Applied Probability, 2017
- A Copula‐Based Non‐parametric Measure of Regression DependenceScandinavian Journal of Statistics, 2012
- Asymptotic Statistics1998
- A Coupling Proof of the Asymptotic Normality of the Permutation OscillationProbability in the Engineering and Informational Sciences, 1995
- Projections onto convex cones in Hilbert spaceJournal of Approximation Theory, 1991
- Order Restricted Statistical InferenceTechnometrics, 1990
- A central limit theorem for m-dependent random variablesDuke Mathematical Journal, 1958