Local linear fitting under near Epoch dependence: Uniform consistency with convergence rates

Degui Li, Zudi Lu, Oliver Linton

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory 23, 37-70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.
Original languageEnglish
Pages (from-to)935 - 958
Number of pages24
JournalEconometric Theory
Volume28
Issue number5
DOIs
Publication statusPublished - 2012

Cite this

Li, Degui ; Lu, Zudi ; Linton, Oliver. / Local linear fitting under near Epoch dependence: Uniform consistency with convergence rates. In: Econometric Theory. 2012 ; Vol. 28, No. 5. pp. 935 - 958.
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Local linear fitting under near Epoch dependence: Uniform consistency with convergence rates. / Li, Degui; Lu, Zudi; Linton, Oliver.

In: Econometric Theory, Vol. 28, No. 5, 2012, p. 935 - 958.

Research output: Contribution to journalArticleResearchpeer-review

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AB - Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory 23, 37-70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

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