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Wavelet Threshold Estimation of a Regression Function with Random Design

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  • Zhang, Shuanglin
  • Wong, Man-Yu
  • Zheng, Zhongguo

Abstract

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space Bsp, q is proved under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a wide range of Besov scale is also constructed.

Suggested Citation

  • Zhang, Shuanglin & Wong, Man-Yu & Zheng, Zhongguo, 2002. "Wavelet Threshold Estimation of a Regression Function with Random Design," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 256-284, February.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:256-284
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    References listed on IDEAS

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    1. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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    Cited by:

    1. Michael Levine, 2019. "Robust functional estimation in the multivariate partial linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 743-770, August.

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