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An extension of Chesneau’s theorem

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  • Kou, Junke
  • Liu, Youming

Abstract

This paper considers a lower bound estimation over Lp(Rd)(1≤p<∞) risk for d dimensional regression functions in Besov spaces based on biased data. We provide the best possible lower bound up to a lnn factor by using wavelet methods. When the weight function ω(x,y)≡1 and d=1, our result reduces to Chesneau’s theorem, see Chesneau (2007).

Suggested Citation

  • Kou, Junke & Liu, Youming, 2016. "An extension of Chesneau’s theorem," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 23-32.
    • Handle: RePEc:eee:stapro:v:108:y:2016:i:c:p:23-32
    DOI: 10.1016/j.spl.2015.09.018
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    References listed on IDEAS

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    1. Yogendra P. Chaubey & Christophe Chesneau & Esmaeil Shirazi, 2013. "Wavelet-based estimation of regression function for dependent biased data under a given random design," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 53-71, March.
    2. J. Cristóbal & J. Ojeda & J. Alcalá, 2004. "Confidence bands in nonparametric regression with length biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 475-496, September.
    3. 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.
    4. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
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    Citations

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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. 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.

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