Two-time-scale nonparametric recursive regression estimator for independent functional data

Abstract

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets.

Keywords:

• Functional data
• nonparametric regression estimation
• stochastic approximation algorithm
• smoothing
• curve fitting
• two-time-Scale approximation algorithm

2010 MATHEMATICS SUBJECT CLASSIFICATION::

• Primary 62G08
• 62L20
• Secondary 65D10