On asymptotically optimal wavelet estimation of trend functions under long-range dependence

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2012
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Shumeyko, Yevgen
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Bernoulli. 2012, 18(1), pp. 137-176. ISSN 1350-7265. Available under: doi: 10.3150/10-BEJ332
Zusammenfassung

We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and resolution parameters are derived. Due to adaptation to the properties of the underlying trend function, the approach shows very good performance for smooth trend functions while remaining competitive with minimax wavelet estimation for functions with discontinuities. Simulations illustrate the asymptotic results and finite-sample behavior.

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Fachgebiet (DDC)
510 Mathematik
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long-range dependence, mean integrated squared error, nonparametric regression, thresholding, trend estimation, wavelet
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ISO 690BERAN, Jan, Yevgen SHUMEYKO, 2012. On asymptotically optimal wavelet estimation of trend functions under long-range dependence. In: Bernoulli. 2012, 18(1), pp. 137-176. ISSN 1350-7265. Available under: doi: 10.3150/10-BEJ332
BibTex
@article{Beran2012asymp-23239,
  year={2012},
  doi={10.3150/10-BEJ332},
  title={On asymptotically optimal wavelet estimation of trend functions under long-range dependence},
  number={1},
  volume={18},
  issn={1350-7265},
  journal={Bernoulli},
  pages={137--176},
  author={Beran, Jan and Shumeyko, Yevgen}
}
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