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Type of Publication:  Journal article 
Author:  Feng, Yuanhua; Beran, Jan 
Year of publication:  2013 
Published in:  Journal of Time Series Analysis ; 34 (2013), 1.  pp. 3039.  ISSN 01439782.  eISSN 14679892 
DOI (citable link):  https://dx.doi.org/10.1111/j.14679892.2012.00811.x 
Summary: 
Consider the estimation of g(ν), the νth derivative of the mean function, in a fixeddesign nonparametric 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 nonparametric regression with iid errors.

Subject (DDC):  310 Statistics 
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FENG, Yuanhua, Jan BERAN, 2013. Optimal convergence rates in nonparametric regression with fractional time series errors. In: Journal of Time Series Analysis. 34(1), pp. 3039. ISSN 01439782. eISSN 14679892. Available under: doi: 10.1111/j.14679892.2012.00811.x
@article{Feng2013Optim24965, title={Optimal convergence rates in nonparametric regression with fractional time series errors}, year={2013}, doi={10.1111/j.14679892.2012.00811.x}, number={1}, volume={34}, issn={01439782}, journal={Journal of Time Series Analysis}, pages={3039}, author={Feng, Yuanhua and Beran, Jan} }