In: Stochastic Processes & Their Applications, 91 (2001), pp. 277-308. ISSN 0304-4149
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Abstract
We fit a class of semiparametric models to a nonstationary process. This class is parametrized by a mean function µ( · ) and a p-dimensional function theta ( · ) = (theta(1)( · ) , ..., theta(p) ( · ))´ that parametrizes the time-varying spectral density ftheta( · ) (lambda). Whereas the mean function is estimated by a usual kernel estimator, each component of theta ( · ) is estimated by a nonlinear wavelet method. According to a truncated wavelet series expansion of theta(i) ( · ), we define empirical versions of the corresponding wavelet coefficients by minimizing an empirical version of the Kullback-Leibler distance. In the main smoothing step, we perform nonlinear thresholding on these coefficients, which finally provides a locally adaptive estimator of theta(i) ( · ). This method is fully automatic and adapts to different smoothness classes. It is shown that usual rates of convergence in Besov smoothness classes are attained up to a logarithmic factor.
Document type: | Article |
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Journal or Publication Title: | Stochastic Processes & Their Applications |
Volume: | 91 |
Publisher: | Elsevier |
Place of Publication: | Amsterdam |
Date Deposited: | 25 May 2016 12:59 |
Date: | 2001 |
ISSN: | 0304-4149 |
Page Range: | pp. 277-308 |
Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Uncontrolled Keywords: | Locally stationary processes; Nonlinear thresholding; Nonparametric curve estimation; Preperiodogram; Time series; Wavelet estimators |
Series: | Beiträge zur Statistik > Beiträge |