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A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

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  • Christophe Chesneau

Abstract

We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions.

Suggested Citation

  • Christophe Chesneau, 2014. "A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jijmms:195765
    DOI: 10.1155/2014/195765
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    References listed on IDEAS

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    1. Jarrow, Robert & Ruppert, David & Yu, Yan, 2004. "Estimating the Interest Rate Term Structure of Corporate Debt With a Semiparametric Penalized Spline Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 57-66, January.
    2. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    3. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    4. 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.
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