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L1-rate of convergence of smoothed histogram

Author

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  • Bouezmarni, T.
  • Mesfioui, M.
  • Rolin, J.M.

Abstract

We consider the smoothed histograms by gamma densities for an i.i.d. sample defined on the positive real line. Under sufficient conditions on the bandwidth and the density function, we obtain the asymptotic behavior, the lower and upper bound of the expected average absolute error of this estimator. The results of a simulation demonstrate the excellent performance of the gamma histogram.

Suggested Citation

  • Bouezmarni, T. & Mesfioui, M. & Rolin, J.M., 2007. "L1-rate of convergence of smoothed histogram," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1497-1504, August.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:14:p:1497-1504
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    References listed on IDEAS

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    1. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    2. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(2), pages 390-412, April.
    3. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    4. W. Gawronski & U. Stadtmüller, 1981. "Smoothing histograms by means of lattice-and continuous distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 28(1), pages 155-164, December.
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    Cited by:

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