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Block thresholding for density estimation: local and global adaptivity

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  • Chicken, Eric
  • Cai, T. Tony

Abstract

We consider wavelet block thresholding method for density estimation. A block-thresholded density estimator is proposed and is shown to achieve optimal global rate of convergence over Besov spaces and simultaneously attain the optimal adaptive pointwise convergence rate as well. These results are obtained in part through the determination of an optimal block length.

Suggested Citation

  • Chicken, Eric & Cai, T. Tony, 2005. "Block thresholding for density estimation: local and global adaptivity," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 76-106, July.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:76-106
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    References listed on IDEAS

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    1. Efromovich, Sam, 1994. "On adaptive estimation of nonlinear functionals," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 57-63, January.
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    Cited by:

    1. Bulla, Ingo & Chesneau, Christophe & Navarro, Fabien & Mark, Tanya, 2015. "A note on the adaptive estimation of a bi-dimensional density in the case of knowledge of the copula density," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 6-13.
    2. Renyu Ye & Xinsheng Liu & Yuncai Yu, 2020. "Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    3. Karol Dziedziul & Magdalena Kucharska & Barbara Wolnik, 2011. "Estimation of the smoothness of density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 991-1001.
    4. Li, Linyuan, 2008. "On the block thresholding wavelet estimators with censored data," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1518-1543, September.
    5. Efromovich, Sam, 2011. "Nonparametric estimation of the anisotropic probability density of mixed variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 468-481, March.
    6. Li, Linyuan, 2015. "Nonparametric adaptive density estimation on random fields using wavelet method," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 346-355.
    7. Krebs, Johannes T.N., 2018. "Nonparametric density estimation for spatial data with wavelets," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 300-319.
    8. Steigerwald, Douglas G, 2006. "A Note on Adaptive Estimation," University of California at Santa Barbara, Economics Working Paper Series qt94v9g27p, Department of Economics, UC Santa Barbara.
    9. Christophe Chesneau & Fabien Navarro, 2017. "On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator," Working Papers 2017-68, Center for Research in Economics and Statistics.
    10. Chen, Di-Rong & Cheng, Kun & Liu, Chao, 2022. "Framelet block thresholding estimator for sparse functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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