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

Beran, Jan; Shumeyko, Yevgen

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

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Datum

2012

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

long-range dependence, mean integrated squared error, nonparametric regression, thresholding, trend estimation, wavelet

Zitieren

ISO 690

BERAN, 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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Universitätsbibliographie

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