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LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES

Published online by Cambridge University Press:  27 April 2012

Degui Li ,
Zudi Lu  and
Oliver Linton
Degui Li
Affiliation:
Monash University
Zudi Lu
Affiliation:
University of Adelaide
Oliver Linton*
Affiliation:
University of Cambridge
*
*Address correspondence to Oliver Linton, Faculty of Economics, Cambridge, CB3 9DD, United Kingdom; e-mail: obl20@cam.ac.uk.
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Abstract

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 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.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 935 - 958
Copyright
Copyright © Cambridge University Press 2012

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