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M-estimation in nonparametric regression under strong dependence and infinite variance

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Abstract

A robust local linear regression smoothing estimator for a nonparametric regression model with heavy-tailed dependent errors is considered in this paper. Under certain regularity conditions, the weak consistency and asymptotic distribution of the proposed estimators are obtained. If the errors are short-range dependent, then the limiting distribution of the estimator is normal. If the data are long-range dependent, then the limiting distribution of the estimator is a stable distribution.

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Authors and Affiliations

  1. Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Ngai Hang Chan

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Rongmao Zhang

Authors
  1. Ngai Hang Chan
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  2. Rongmao Zhang
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Correspondence to Ngai Hang Chan.

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Chan, N.H., Zhang, R. M-estimation in nonparametric regression under strong dependence and infinite variance. Ann Inst Stat Math 61, 391–411 (2009). https://doi.org/10.1007/s10463-007-0142-4

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  • DOI: https://doi.org/10.1007/s10463-007-0142-4

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