Optimal convergence rates in non-parametric regression with fractional time series errors

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2013
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Journal of Time Series Analysis. 2013, 34(1), pp. 30-39. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/j.1467-9892.2012.00811.x
Zusammenfassung

Consider the estimation of g(ν), the νth derivative of the mean function, in a fixed-design non-parametric regression model with stationary time series errors ξi. We assume that , ξi are obtained by applying an invertible linear filter to iid innovations, and the spectral density of ξi has the form as λ → 0 with constants cf > 0 and α ∈ (−1,1). Under regularity conditions, the optimal convergence rate of is shown to be with r = (1 − α)(k − ν)/(2k+1 − α). This rate is achieved by local polynomial fitting. Moreover, in spite of including long memory and antipersistence, the required conditions on the innovation distribution turn out to be the same as in non-parametric regression with iid errors.

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ISO 690FENG, Yuanhua, Jan BERAN, 2013. Optimal convergence rates in non-parametric regression with fractional time series errors. In: Journal of Time Series Analysis. 2013, 34(1), pp. 30-39. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/j.1467-9892.2012.00811.x
BibTex
@article{Feng2013Optim-24965,
  year={2013},
  doi={10.1111/j.1467-9892.2012.00811.x},
  title={Optimal convergence rates in non-parametric regression with fractional time series errors},
  number={1},
  volume={34},
  issn={0143-9782},
  journal={Journal of Time Series Analysis},
  pages={30--39},
  author={Feng, Yuanhua and Beran, Jan}
}
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    <dcterms:abstract xml:lang="eng">Consider the estimation of g(ν), the νth derivative of the mean function, in a fixed-design non-parametric regression model with stationary time series errors ξi. We assume that , ξi are obtained by applying an invertible linear filter to iid innovations, and the spectral density of ξi has the form as λ → 0 with constants cf &gt; 0 and α  ∈  (−1,1). Under regularity conditions, the optimal convergence rate of is shown to be with r = (1 − α)(k − ν)/(2k+1 − α). This rate is achieved by local polynomial fitting. Moreover, in spite of including long memory and antipersistence, the required conditions on the innovation distribution turn out to be the same as in non-parametric regression with iid errors.</dcterms:abstract>
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