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Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators

Author

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  • Matthias HAGMANN

    (HEC-University of Lausanne and FAME)

  • Olivier SCAILLET

    (HEC-University of Geneva and FAME)

Abstract

We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0, ¥). We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.

Suggested Citation

  • 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.
    • Handle: RePEc:fam:rpseri:rp91
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    References listed on IDEAS

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    3. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
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    Citations

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    Cited by:

    1. 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.
    2. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
    3. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    4. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    5. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    6. Marcelo Fernandes & Eduardo Mendes & Olivier Scaillet, 2015. "Testing for symmetry and conditional symmetry using asymmetric kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 649-671, August.
    7. Masayuki Hirukawa & Mari Sakudo, 2015. "Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 41-63, March.
    8. Hirukawa, Masayuki & Sakudo, Mari, 2019. "Another bias correction for asymmetric kernel density estimation with a parametric start," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 158-165.
    9. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    10. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    11. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    12. Juxia Xiao & Xu Li & Jianhong Shi, 2019. "Local linear smoothers using inverse Gaussian regression," Statistical Papers, Springer, vol. 60(4), pages 1225-1253, August.
    13. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    14. Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.
    15. Charpentier, Arthur & Flachaire, Emmanuel, 2015. "Log-Transform Kernel Density Estimation Of Income Distribution," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 141-159, Mars-Juin.
    16. El Ghouch, Anouar & Genton, Marc G., 2009. "Local Polynomial Quantile Regression With Parametric Features," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1416-1429.
    17. Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 357-379, April.
    18. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.

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    More about this item

    Keywords

    semiparametric density estimation; asymmetric kernel; income distribution; loss distribution; health insurance; specification testing;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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