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Loch linear fitting under near epoch dependence: uniform consistency with convergence rate

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  • Li, Degui
  • Lu, Zudi
  • Linton, Oliver

Abstract

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

Suggested Citation

  • Li, Degui & Lu, Zudi & Linton, Oliver, 2010. "Loch linear fitting under near epoch dependence: uniform consistency with convergence rate," LSE Research Online Documents on Economics 58160, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:58160
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    More about this item

    Keywords

    α − mixing; local linear fitting; near epoch dependence; convergence rates; uniform consistency;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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