Generalized linear model with functional predictors and their derivatives

Aziza Ahmedou, Jean-Marie Marion and Besnik Pumo

Journal of Multivariate Analysis, 2016, vol. 146, issue C, 313-324

Abstract: The conditional expectation E(Y|X) of a generalized functional linear model with scalar response Y is given by g{〈X,ϕ〉L2} where X and ϕ are functions defined in L2:=L2[0,1]. Let us consider that X belongs to the Sobolev space W:=W2,1[0,1] and denote X′ its derivative. In this paper we focus on an extension of the previous model where E(Y|X) is given by g{〈X,β〉W+〈X′,γ〉L2}. With a similar approach to Cardot and Sarda (2005) or Stone (1986) for generalized additive models, we propose estimators for the unknown parameters β, γ and obtain their rate of convergence. We compare numerically the prediction performance of this new model with alternative models proposed in the literature.

Keywords: Generalized functional linear model; Derivative component model (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2015.10.009

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