Recursive estimation of nonparametric regression with functional covariate.

Aboubacar Amiri (1) , Christophe Crambes (2) , Baba Thiam (1)

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

The main purpose of this work is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and a real data set study.

Keywords: asymptotic normality; Functional data; recursive kernel estimators; regression function; quadratic error; almost sure convergence; asymptotic normality.

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Aboubacar Amiri, Christophe Crambes, Baba Thiam. Recursive estimation of nonparametric regression with functional covariate.. 2012. ⟨hal-00750894⟩