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Linear wavelet estimation of the derivatives of a regression function based on biased data

Author

Listed:
  • Yogendra P. Chaubey

    (Department of Mathematics and Statistics, Concordia University)

  • Christophe Chesneau

    (Université de Caen; LMNO)

  • Fabien Navarro

    (CREST; ENSAI)

Abstract

This paper deals with the problem of estimating the derivatives of a regression function based on biased data. We develop two different linear wavelet estimators according to the knowledge of the ”biased density” of the design. The new estimators are analyzed with respect to their Lp risk with p>1 over Besov balls. Fast polynomial rates of convergence are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:crs:wpaper:2017-70
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    References listed on IDEAS

    as
    1. José Cristóbal & José Alcalá, 2001. "An overview of nonparametric contributions to the problem of functional estimation from biased data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 309-332, December.
    2. Ahmad, Ibrahim A., 1995. "On multivariate kernel estimation for samples from weighted distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 121-129, February.
    3. Marianna Pensky & Brani Vidakovic, 2001. "On Non-Equally Spaced Wavelet Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 681-690, December.
    4. 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.
    5. 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.
    6. 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.
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