Econometric Theory

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

Degui Lia1, Zudi Lua2 and Oliver Lintona3 c1

a1 Monash University

a2 University of Adelaide

a3 University of Cambridge

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.

Correspondence:

c1 Address correspondence to Oliver Linton, Faculty of Economics, Cambridge, CB3 9DD, United Kingdom; e-mail: obl20@cam.ac.uk.

Footnotes

  The authors thank the co-editor Yoon-Jae Whang and two referees for their valuable comments, which substantially improved the earlier version of this paper. This research was partially supported by Discovery Project and Future Fellowship grants from the Australian Research Council, and the European Research Council.

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