Recursive kernel regression estimation under α – mixing data

Abstract

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs.

Keywords:

• Asymptotic normality
• bandwidth selection
• regression estimation
• recursive kernel estimators
• mixing data
• stochastic approximation algorithm

AMS SUBJECT CLASSIFICATIONS:

• 62G05
• 62G08
• 62G20
• 62L20
• 62H20
• 65D10