Recursive estimation of nonparametric regression with functional covariate

Aboubacar Amiri (1) , Christophe Crambes (2) , Baba Thiam (3)

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 UMR CNRS 8179

The main purpose 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 real dataset studies.

Mots clés: Asymptotic normality; Functional data; Recursive kernel estimators; Regression function; Quadratic error; Almost sure convergence

Domaines: Mathématiques [math]; Statistiques [math.ST]

Aboubacar Amiri, Christophe Crambes, Baba Thiam. Recursive estimation of nonparametric regression with functional covariate. Computational Statistics and Data Analysis, 2014, 69, pp.154 - 172. ⟨10.1016/j.csda.2013.07.030⟩. ⟨hal-01818838⟩