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Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors

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2002

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Annals of the Institute of Statistical Mathematics. 2002, 54(2), pp. 291-311. ISSN 0020-3157. eISSN 1572-9052. Available under: doi: 10.1023/A:1022469818068

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Local polynomial smoothing for the trend function and its derivatives in nonparametric regression with long-memory, short-memory and antipersistent errors is considered. We show that in the case of antipersistence, the convergence rate of a nonparametric regression estimator is faster than for uncorrelated or short-range dependent errors. Moreover, it is shown that unified asymptotic formulas for the optimal bandwidth and the MSE hold for all of the three dependence structures. Also, results on estimation at the boundary are included. A bandwidth selector for nonparametric regression with different types of dependent errors is proposed. Its asymptotic property is investigated. The practical performance of the proposal is illustrated by simulated and real data examples.

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510 Mathematik

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ISO 690BERAN, Jan, Yuanhua FENG, 2002. Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors. In: Annals of the Institute of Statistical Mathematics. 2002, 54(2), pp. 291-311. ISSN 0020-3157. eISSN 1572-9052. Available under: doi: 10.1023/A:1022469818068
BibTex
@article{Beran2002Local-27497,
  year={2002},
  doi={10.1023/A:1022469818068},
  title={Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors},
  number={2},
  volume={54},
  issn={0020-3157},
  journal={Annals of the Institute of Statistical Mathematics},
  pages={291--311},
  author={Beran, Jan and Feng, Yuanhua}
}
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