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Adaptive Estimation of a Density Function using Beta Kernels

Author

Listed:
  • Karine Bertin

    (CIMFAV, Universidad de Valparaiso)

  • Nicolas Klutchnikoff

    (CREST-ENSAI, Université de Strasbourg)

Abstract

In this paper we are interested in the estimation of a density—defined on a compact interval of R—from n independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator using simulated data

Suggested Citation

  • Karine Bertin & Nicolas Klutchnikoff, 2014. "Adaptive Estimation of a Density Function using Beta Kernels," Working Papers 2014-08, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2014-08
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    References listed on IDEAS

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    1. Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," IDEI Working Papers 633, Institut d'Économie Industrielle (IDEI), Toulouse.
    2. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen VK, 2010. "Nonparametric density estimation for multivariate bounded data," LIDAM Reprints CORE 2301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Gustafsson, J. & Hagmann, M. & Nielsen, J. P. & Scaillet, O., 2009. "Local Transformation Kernel Density Estimation of Loss Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 161-175.
    4. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    5. Renault, Olivier & Scaillet, Olivier, 2004. "On the way to recovery: A nonparametric bias free estimation of recovery rate densities," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2915-2931, December.
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    Cited by:

    1. Bertin, Karine & Genest, Christian & Klutchnikoff, Nicolas & Ouimet, Frédéric, 2023. "Minimax properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.
    4. Funke, Benedikt & Kawka, Rafael, 2015. "Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 148-162.

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