Regression estimation by local polynomial fitting for multivariate data streams

Aboubacar Amiri (1) , Baba Thiam (1)

1 LEM - Lille économie management - UMR 9221

In this paper we study a local polynomial estimator of the regression function and its derivatives. We propose a sequential technique based on a multivariate counterpart of the stochastic approximation method for successive experiments for the local polynomial estimation problem. We present our results in a more general context by considering the weakly dependent sequence of stream data, for which we provide an asymptotic bias-variance decomposition of the considered estimator. Additionally, we study the asymptotic normality of the estimator and we provide algorithms for the practical use of the method in data streams framework.

Mots clés: Stochastic approximation; Data streams; Weakly dependent sequences; Kernel methods; Local polynomial

Domaines: Méthodes et statistiques

Aboubacar Amiri, Baba Thiam. Regression estimation by local polynomial fitting for multivariate data streams. Statistical Papers, 2016, 59, pp.813-843. ⟨10.1007/s00362-016-0791-6⟩. ⟨hal-01592783⟩