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Wavelet estimation for samples with random uniform design

Author

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  • Cai, T. Tony
  • Brown, Lawrence D.

Abstract

We show that for nonparametric regression if the samples have random uniform design, the wavelet method with universal thresholding can be applied directly to the samples as if they were equispaced. The resulting estimator achieves within a logarithmic factor from the minimax rate of convergence over a family of Hölder classes. Simulation result is also discussed.

Suggested Citation

  • Cai, T. Tony & Brown, Lawrence D., 1999. "Wavelet estimation for samples with random uniform design," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 313-321, April.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:3:p:313-321
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    Citations

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    Cited by:

    1. Fabien Navarro & Adrien Saumard, 2017. "Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases," Working Papers 2017-67, Center for Research in Economics and Statistics.
    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. Oleg Shestakov, 2020. "Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise," Mathematics, MDPI, vol. 8(3), pages 1-8, March.
    4. Fabien Navarro & Adrien Saumard, 2017. "E?ciency of the V-fold model selection for localized bases," Working Papers 2017-65, Center for Research in Economics and Statistics.
    5. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    6. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2022. "Penalized wavelet estimation and robust denoising for irregular spaced data," Computational Statistics, Springer, vol. 37(4), pages 1621-1651, September.
    7. 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.
    8. Michel H. Montoril & Woojin Chang & Brani Vidakovic, 2019. "Wavelet-Based Estimation of Generalized Discriminant Functions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 318-349, December.
    9. Christophe Chesneau & Salima El Kolei & Junke Kou & Fabien Navarro, 2019. "Nonparametric estimation in a regression model with additive and multiplicative noise," Papers 1906.07695, arXiv.org, revised Jun 2020.
    10. Zeng, Jing & Wang, Zhenjun & Chen, Guobin, 2021. "Biological characteristics of energy conversion in carbon fixation by microalgae," Renewable and Sustainable Energy Reviews, Elsevier, vol. 152(C).
    11. 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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