RECURSIVE ESTIMATION OF REGRESSION FUNCTIONS BY LOCAL POLYNOMIAL FITTING

J. A. VILAR-FERNÁNDEZ AND J. M. VILAR-FERNÁNDEZ

Departamento de Matemáticas, Facultad de Informática, Universidad de A Coruña, 15071 A Coruña, Spain

(Received March 6, 1996; revised October 27, 1997)

Abstract. The recursive estimation of the regression function m(x) = E(Y/X = x) and its derivatives is studied under dependence conditions. The examined method of nonparametric estimation is a recursive version of the estimator based on locally weighted polynomial fitting, that in recent articles has proved to be an attractive technique and has advantages over other popular estimation techniques. For strongly mixing processes, expressions for the bias and variance of these estimators are given and asymptotic normality is established. Finally, a simulation study illustrates the proposed estimation method.

Key words and phrases: Recursive nonparametric estimation, regression models, local polynomial fitting, strongly mixing processes.