B1707
Title: Measuring dependence between a scalar response and a functional covariate
Authors: Daniel Strenger - Graz University of Technology (Austria) [presenting]
Siegfried Hoermann - Graz University of Technology (Austria)
Abstract: The aim is to extend the scope of a recently introduced dependence coefficient between scalar responses and multivariate covariates to the case of functional covariates. While formally the extension is straightforward, the limiting behaviour of the sample version of the coefficient is delicate. It crucially depends on the nearest-neighbour structure of the covariate sample. Essentially, one needs an upper bound for the maximal number of points which share the same nearest neighbour. While a deterministic bound exists for multivariate data, this is no longer the case in infinite dimensional spaces. Surprisingly, very little seems to be known about the properties of the nearest neighbour graph in a high-dimensional or even functional random sample, and hence the main contribution is to advise a way to overcome this problem. An important application of the theoretical results is a test for independence between scalar responses and functional covariates.
