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Adaptive Wavelet Estimations in the Convolution Structure Density Model

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  • Kaikai Cao

    (School of Mathematics and Information Science, Weifang University, Weifang 261061, China)

  • Xiaochen Zeng

    (School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

Abstract

Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal L p risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat. 2019 , 47 , 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

Suggested Citation

  • Kaikai Cao & Xiaochen Zeng, 2020. "Adaptive Wavelet Estimations in the Convolution Structure Density Model," Mathematics, MDPI, vol. 8(9), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1391-:d:401236
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    References listed on IDEAS

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    1. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
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