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Random design wavelet curve smoothing

Author

Listed:
  • Antoniadis, A.
  • Grégoire, G.
  • Vial, P.

Abstract

Common wavelet-based methods for nonparametric regression estimation are difficult to apply when the design is random. This paper proposes a modification of the linear wavelet estimator, called the binned wavelet estimator leading to a fast method with asymptotic properties identical with those of linear wavelet estimators under a fixed equidistant design.

Suggested Citation

  • Antoniadis, A. & Grégoire, G. & Vial, P., 1997. "Random design wavelet curve smoothing," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 225-232, October.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:3:p:225-232
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    Citations

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    Cited by:

    1. 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.
    2. Luz M. Gómez & Rogério F. Porto & Pedro A. Morettin, 2021. "Nonparametric regression with warped wavelets and strong mixing processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1203-1228, December.
    3. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    4. Maarten Jansen & Guy P. Nason & B. W. Silverman, 2009. "Multiscale methods for data on graphs and irregular multidimensional situations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 97-125, January.
    5. Antoniadis, Anestis & Bigot, Jéremie & Gijbels, Irène, 2007. "Penalized wavelet monotone regression," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1608-1621, October.
    6. Christophe Chesneau & Jalal Fadili, 2012. "Adaptive wavelet estimation of a function in an indirect regression model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 25-46, January.

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