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Nonparametric Wavelet Regression Based on Biased Data

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  • Christophe Chesneau
  • Esmaeil Shirazi

Abstract

The estimation of the regression function in the biased nonparametric regression model is investigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls.

Suggested Citation

  • Christophe Chesneau & Esmaeil Shirazi, 2014. "Nonparametric Wavelet Regression Based on Biased Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2642-2658, July.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:13:p:2642-2658
    DOI: 10.1080/03610926.2012.681536
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    Cited by:

    1. Jia Chen & Junke Kou, 2023. "Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule," Mathematics, MDPI, vol. 12(1), pages 1-10, December.
    2. Kou, Junke & Liu, Youming, 2016. "An extension of Chesneau’s theorem," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 23-32.
    3. Junke Kou & Youming Liu, 2018. "Wavelet regression estimations with strong mixing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 667-688, December.
    4. Yogendra P. Chaubey & Christophe Chesneau & Fabien Navarro, 2017. "Linear wavelet estimation of the derivatives of a regression function based on biased data," Working Papers 2017-70, Center for Research in Economics and Statistics.

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