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Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval

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  • Hirukawa, Masayuki
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    Abstract

    This paper demonstrates that two classes of multiplicative bias correction (MBC) techniques, originally proposed for density estimation using symmetric second-order kernels by Terrell and Scott (1980) and Jones et al. (1995), can be applied to density estimation using the beta and modified beta kernels. It is shown that, under sufficient smoothness of the true density, both MBC techniques reduce the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. Accordingly, mean squared errors of these MBC estimators achieve a faster convergence rate of O(n-8/9) for the interior part, when best implemented. Furthermore, the estimators always generate nonnegative density estimates by construction. To implement the MBC estimators, a plug-in smoothing parameter choice method is proposed. Monte Carlo simulations indicate good finite sample performance of the estimators.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 2 (February)
    Pages: 473-495

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:473-495

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    Web page: http://www.elsevier.com/locate/csda

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    1. Matthias HAGMANN & Olivier SCAILLET, 2003. "Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators," FAME Research Paper Series rp91, International Center for Financial Asset Management and Engineering.
    2. Christian Gourieroux & Alain Monfort, 2006. "(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution," Working Papers 2006-31, Centre de Recherche en Economie et Statistique.
    3. Masayuki Hirukawa, 2006. "A Modified Nonparametric Prewhitened Covariance Estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 441-476, 05.
    4. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
    5. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    6. 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.
    7. Bruce M. Brown, 1999. "Beta-Bernstein Smoothing for Regression Curves with Compact Support," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(1), pages 47-59.
    8. Olivier RENAULT & Olivier SCAILLET, 2003. "On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities," FAME Research Paper Series rp83, International Center for Financial Asset Management and Engineering.
    9. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    10. M.C. Jones & D.A. Henderson, 2007. "Miscellanea Kernel-Type Density Estimation on the Unit Interval," Biometrika, Biometrika Trust, vol. 94(4), pages 977-984.
    11. Jens Perch Nielsen, 2001. "Boundary and Bias Correction in Kernel Hazard Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(4), pages 675-698.
    12. Linton, Oliver & Nielsen, Jens Perch, 1994. "A multiplicative bias reduction method for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 181-187, February.
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    Cited by:
    1. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," Articles of International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.

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