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Loch Linear Fitting under Near Epoch Dependence: Uniform Consistency with Convergence Rate

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  • Degui Li
  • Oliver Linton
  • Zudi Lu

Abstract

Local linear fitting is a popular nonparametric method in nonlinear statistical andeconometric modelling. Lu and Linton (2007) established the point wise asymptoticdistribution (central limit theorem) for the local linear estimator of nonparametricregression function under the condition of near epoch dependence. We furtherinvestigate the uniform consistency of this estimator. The uniformly strong andweak consistencies with convergence rates for the local linear fitting areestablished under mild conditions. Furthermore, general results of uniformconvergence rates for nonparametric kernel-based estimators are provided.Applications of our results to conditional variance function estimation and someeconomic time series models are also discussed. The results of this paper will beof widely potential interest in time series semiparametric modelling.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2010/549.

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Date of creation: Aug 2010
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Handle: RePEc:cep:stiecm:/2010/549

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Keywords: local linear fitting; near epoch dependence; convergence rates; uniform consistency.;

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