A Kendall correlation coefficient for functional dependence

Abstract

Measuring dependence is a basic question when dealing with functional observations. The usual correlation for curves is not robust. Kendall's coefficient is a natural description of dependence between finite dimensional random variables. We extend this concept to functional observations. Given a bivariate sample of functions, a robust analysis of dependence can be carried out through the functional version of a Kendall correlation coefficient introduced in this paper. We also study its statistical properties and provide several applications to both simulated and real data, including asset portfolios in finance and microarray time series in genetics