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Locally modelled regression and functional data

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  • J. Barrientos-Marin
  • F. Ferraty
  • P. Vieu

Abstract

The general framework of this paper deals with the nonparametric regression of a scalar response on a functional variable (i.e. one observation can be a curve, surface, or any other object lying into an infinite-dimensional space). This paper proposes to model local behaviour of the regression operator (i.e. the link between a scalar response and an explanatory functional variable). To this end, one introduces a functional approach in the same spirit as local linear ideas in nonparametric regression. The main advantage of this functional local method is to propose an explicit expression of a kernel-type estimator which makes its computation easy and fast while keeping good predictive performance. Asymptotic properties are stated, and a functional data set illustrates the good behaviour of this functional locally modelled regression method.

Suggested Citation

  • J. Barrientos-Marin & F. Ferraty & P. Vieu, 2010. "Locally modelled regression and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 617-632.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:617-632
    DOI: 10.1080/10485250903089930
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