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Wavelet density estimation by approximation of log-densities

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  • Koo, Ja-Yong
  • Kim, Woo-Chul

Abstract

Probability density estimation is considered when log-density function belongs to the Besov function class Bspq. It is shown that n-2s/(2s+1) is a lower rate of convergence in Kullback-Leibler distance. Density functions are estimated by the maximum likelihood method in sequences of regular exponential families based on wavelet basis functions.

Suggested Citation

  • Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:3:p:271-278
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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. Kerkyacharian, Gérard & Picard, Dominique, 1993. "Density estimation by kernel and wavelets methods: Optimality of Besov spaces," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 327-336, November.
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    1. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    2. Bak, Kwan-Young & Jhong, Jae-Hwan & Lee, JungJun & Shin, Jae-Kyung & Koo, Ja-Yong, 2021. "Penalized logspline density estimation using total variation penalty," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    3. Song, Seongjoo, 2010. "Lévy density estimation via information projection onto wavelet subspaces," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1623-1632, November.
    4. Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log‐density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 749-763, December.
    5. Koo, Ja-Yong, 1998. "Convergence Rates for Logspline Tomography," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 367-384, November.

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