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Wavelet-based estimation of regression function for dependent biased data under a given random design

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  • Yogendra P. Chaubey
  • Christophe Chesneau
  • Esmaeil Shirazi

Abstract

In this article, we consider the estimation of the regression function in a dependent biased model. It is assumed that the observations form a stationary α-mixing sequence. We introduce a new estimator based on a wavelet basis. We explore its asymptotic performances via the supremum norm error and the mean integrated squared error. Fast rates of convergence are established.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:53-71
    DOI: 10.1080/10485252.2012.734619
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    Cited by:

    1. Huijun Guo & Youming Liu, 2017. "Strong consistency of wavelet estimators for errors-in-variables regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 121-144, February.
    2. Huijun Guo & Youming Liu, 2019. "Regression estimation under strong mixing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 553-576, June.
    3. 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.
    4. Kou, Junke & Liu, Youming, 2016. "An extension of Chesneau’s theorem," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 23-32.
    5. 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.
    6. 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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