Consistency of the regression estimator with functional data under long memory conditions

Karim Benhenni (1) , Sonia Hedli-Griche (2) , Mustapha Rachdi (2) , Philippe Vieu (3)

1 MS3 - Méthodologie Statistique et Sciences Sociales
2 SFS - Statistique Fonctionnelle & Sondages
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the nonparametric regression estimation when the explanatory variable takes values in some abstract functional space. We establish some asymptotic results and we give the (pointwise and uniform) convergence of the kernel type estimator constructed from functional data under long memory conditions.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Karim Benhenni, Sonia Hedli-Griche, Mustapha Rachdi, Philippe Vieu. Consistency of the regression estimator with functional data under long memory conditions. Statistics and Probability Letters, 2008, 78 (8), pp.1043-1049. ⟨10.1016/j.spl.2007.11.011⟩. ⟨hal-00622143⟩