On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths |
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Authors: | Carlos Martins-Filho Paulo Saraiva |
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Institution: | 1. Department of Economics , University of Colorado , Boulder , Colorodo , USA;2. IFPRI , Washington , D.C. , USA carlos.martins@colorado.edu;4. Department of Economics , University of Colorado , Boulder , Colorodo , USA |
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Abstract: | Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995
Boente , G. ,
Fraiman , R. ( 1995 ). Asymptotic distribution of data-driven smoothers in density and regression estimation under dependence . Can. J. Statist. 23 : 383 – 397 .Crossref], Web of Science ®] , Google Scholar]) and Ziegler (2004
Ziegler , K. ( 2004 ). Adaptive kernel estimation of the mode in nonparametric random design regression model . Probab. Mathemat. Statist. 24 : 213 – 235 . Google Scholar]). |
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Keywords: | Asymptotic normality Local polynomial estimation Mixing processes Stochastic bandwidth |
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