COMPSTAT 2016: Start Registration
View Submission - CRoNoS FDA 2016
A0198
Title: Testing the influence of functional variables on functional responses Authors:  Valentin Patilea - CREST Ensai (France) [presenting]
Samuel Maistre - Universite de Strasbourg (France)
Abstract: The considered problem is the test of the effect of Hilbert space-valued covariates on Hilbert space-valued responses. This general framework includes functional regression models checks against general alternatives, as well as testing conditional independence with functional data. The significance test for functional regressors in nonparametric regression with general covariates and scalar or functional responses is another example. We propose a new test based on kernel smoothing. The test statistic is asymptotically standard normal under the null hypothesis provided the smoothing parameter tends to zero at a suitable rate. The one-sided test is consistent against any fixed alternative and detects local alternatives a la Pitman approaching the null hypothesis. In particular we show that neither the dimension of the outcome nor the dimension of the functional covariates influences the theoretical power of the test against such local alternatives. Simulation experiments and a real data application illustrate the performance of the new test with finite samples.