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Point-wise estimation for anisotropic densities

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  • Liu, Youming
  • Wu, Cong

Abstract

This paper considers point-wise estimation of density functions under the local anisotropic Hölder condition by the wavelet method. A linear wavelet estimate is first introduced and shown to be optimal. A data driven version is provided for adaptivity and the influence of the dimension is reduced under the independence structure of the estimated density.

Suggested Citation

  • Liu, Youming & Wu, Cong, 2019. "Point-wise estimation for anisotropic densities," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 112-125.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:112-125
    DOI: 10.1016/j.jmva.2018.11.014
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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.
    2. Walter, Gilbert G., 1999. "Density estimation in the presence of noise," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 237-246, February.
    3. Pensky, Marianna, 2002. "Density deconvolution based on wavelets with bounded supports," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 261-269, February.
    4. Butucea, Cristina, 2000. "The adaptive rate of convergence in a problem of pointwise density estimation," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 85-90, March.
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