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Estimation of the smoothness of density

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Listed:
  • Karol Dziedziul
  • Magdalena Kucharska
  • Barbara Wolnik

Abstract

This paper introduces a definition where the smoothness of a function f is characterized by means of the Besov spaces , that is, there is the parameter s* such that for all ss*, . If f is a density with the smoothness s*, then we construct an estimator of s* which is based on histograms.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:991-1001
    DOI: 10.1080/10485252.2011.587879
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    References listed on IDEAS

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    1. 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.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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