B0905
Title: Goodness-of-fit tests for models with functional data
Authors: Juan A Cuesta-Albertos - Universidad de Cantabria (Spain)
Eduardo Garcia-Portugues - Carlos III University of Madrid (Spain)
Manuel Febrero-Bande - University of Santiago de Compostela (Spain)
Wenceslao Gonzalez-Manteiga - University of Santiago de Compostela (Spain) [presenting]
Abstract: Different goodness-of-fit tests for some null hypothesis of models with functional data are given. The simplest versions of these tests are based on the residual marked empirical process indexed by random projections for testing the hypothesis of a functional linear model with scalar response. Some asymptotic distribution of the mentioned projected empirical process is obtained under general conditions using estimation by functional principal components. Other considered models are the functional partially linear model or the functional linear model with functional response. The asymptotic distribution of the Kolmogorv-Smirnov and Cramer-von Mises tests built with the associated process is considered. The exact distribution of the tests is also calibrated by bootstrap and the finite sample properties are illustrated by simulations as well as real data applications.
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