A RKHS-based proporsal for variable selection in functional regression

J. R. Berrendero Díaz, B. Bueno Larraz, A. Cuevas González

We propose a new variable selection methodology for functional regression problems with a scalar response. Our basic tool will be the RKHS (Reproducing Kernel Hilbert Space) associated with the covariance function of the underlying process. Using the so-called Loève's isometry in RKHS, we define the prediction of the response variable in terms of a functional optimization problem. Then, under a natural sparsity assumption, we can find (via an iterative approximation) the most relevant points for the original problem.
The resulting procedure is easy to interpret and allows us to add extra information on the model (regarding, e.g., the covariance structure). We propose also a method to select the number of relevant points. We prove as well that our method fulfills a functional variant of the Sure Screening Property defined by Fan and Lv (2008, JRSS-B). This means that, asymptotically, we will find all the relevant variables with arbitrary precision. Some empirical comparisons are given.

Palabras clave: functional regression, variable selection, RKHS

X09.2 Grupo de Análisis de Datos Funcionales: últimos avances y aplicaciones
7 de septiembre de 2016  17:30
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