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

作     者：Francisco-Fernández, M Vilar-Fernández, JM Vilar-Fernández, JA 

作者机构：Univ A Coruna Fac Informat Dept Matemat La Coruna 15071 Spain 

出 版 物：《COMMUNICATIONS IN STATISTICS-THEORY AND METHODS》 (统计学通讯：理论与方法)

年 卷 期：2003年第32卷第12期

页      面：2415-2440页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：European Regional Development Fund  FEDER  (PGIDIT03PXIC10505PN) 

主　　题：nonparametric regression estimation local polynomial fitting dependent data strong consistency 

摘      要：In this article, 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(l) correlation structure, strong consistency properties are also derived for a modified version of the local polynomial estimators proposed by Vilar-Fernandez and Francisco-Fernandez (Vilar-Fernandez, J. M., Francisco-Fern ndez, M. (2002). Local polynomial regression smoothers with AR-error structure. TEST 11(2):439-464).