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

Author

Listed:
  • Christophe Chesneau

    (Université de Caen; LMNO)

  • Fabien Navarro

    (CREST;ENSAI)

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 nonparametric models including possible dependent observations. We give applications of this result for the nonparametric 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," Working Papers 2017-68, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-68
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    References listed on IDEAS

    as
    1. Felix Abramovich & Claudia Angelini & Daniela Canditiis, 2007. "Pointwise optimality of Bayesian wavelet estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 425-434, September.
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    3. Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    4. Young Truong & Prakash Patil, 2001. "Asymptotics for Wavelet Based Estimates of Piecewise Smooth Regression for Stationary Time Series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 159-178, March.
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