Consistency of the recursive nonparametric regression estimation for dependent functional data.

Aboubacar Amiri (1) , Baba Thiam (1)

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition.

Mots clés: Functional data; recursive kernel estimators; regression function; quadratic mean error; almost sure convergence.; almost sure convergence

Domaines: Théorie [stat.TH]

Aboubacar Amiri, Baba Thiam. Consistency of the recursive nonparametric regression estimation for dependent functional data.. 2013. ⟨hal-00815205⟩