Kendall's Tau for Functional Data Analysis

Understand

We treat the problem of testing for association between a functional variable belonging to Hilbert space and a scalar variable.

• Particularly, we propose a distribution-free test statistic based on Kendall's Tau which is one of the most popular methods to determine the association between two random variables.
• The distribution of the test statistic under the null hypothesis of independence is established using the theory of U-statistics taking values in a Hilbert space.
• We also consider the case when the functional data is sparsely observed, a situation that arises in many applications.