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On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator

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  • Christophe Chesneau
  • Fabien Navarro

Abstract

In this paper we provide a theoretical contribution to the pointwise mean squared error of an adaptive multidimensional term-by-term thresholding wavelet estimator. A general result exhibiting fast rates of convergence under mild assumptions on the model is proved. It can be applied for a wide range of non parametric models including possible dependent observations. We give applications of this result for the non parametric regression function estimation problem (with random design) and the conditional density estimation problem.

Suggested Citation

  • Christophe Chesneau & Fabien Navarro, 2017. "On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(11), pages 5643-5655, June.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:11:p:5643-5655
    DOI: 10.1080/03610926.2015.1107587
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