On the uniform strong consistency of local polynomial regression under dependence conditions

This is a preprint of an article submitted for consideration in the Communications in Statistics, Theory and Methods © 2003 copyright Taylor & Francis ; Communications in Statistics, Theory and Methods is available online at: http://www.informaworld.com/[Abstract] In this paper, nonparametric estimators of the regression function, and its derivatives, obtained by means of weighted local polynomial fitting are studied. Consider the fixed regression model where the error random variables are coming from a stationary stochastic process satisfying a mixing condition. Uniform strong consistency, along with rates, are established for these estimators. Furthermore, when the errors follow an AR(1) correlation structure, strong consistency properties are also derived for a modiÞed version of the local polynomial estimators proposed by Vilar-Fernández and Francisco-Fernández in (1).Ministerio de Ciencia y Tecnología; PGIDT01PXI10505PRMinisterio de Ciencia y Tecnología; PB98-0182-C02-01Ministerio de Ciencia y Tecnología; BFM2002-0026