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Local multiplicative bias correction for asymmetric kernel density estimators

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  • Hagmann, M.
  • Scaillet, O.

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 141 (2007)
Issue (Month): 1 (November)
Pages: 213-249

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Handle: RePEc:eee:econom:v:141:y:2007:i:1:p:213-249

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

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References

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  1. Chen, Song Xi, 1999. "Local linear smoothers using asymmetric kernels," SFB 373 Discussion Papers 1999,100, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Matthias Hagmann & Olivier Scaillet, 2004. "Local Multiplicative Bias Correction For Asymmetric Kernel Density Estimators," Royal Economic Society Annual Conference 2004 25, Royal Economic Society.
  3. 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.
  4. Robert F. Engle, 1996. "The Econometrics of Ultra-High Frequency Data," NBER Working Papers 5816, National Bureau of Economic Research, Inc.
  5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
  6. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  7. 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(02), pages 390-412, April.
  8. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
  9. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
  10. Bolance, Catalina & Guillen, Montserrat & Perch Nielsen, Jens, 2000. "Kernel Density Estimation of Actuarial Loss Functions," Finance Working Papers 00-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  11. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  12. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
  13. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  14. Marcelo Fernandes & Paulo Monteiro, 2005. "Central limit theorem for asymmetric kernel functionals," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(3), pages 425-442, September.
  15. Christian Gourieroux & Joanna Jasiak, 2001. "Local Likelihood Density Estimation and Value at Risk," Working Papers 2001-31, Centre de Recherche en Economie et Statistique.
  16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  17. 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.
  18. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
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Citations

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Cited by:
  1. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2010. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series 2010/19, Center for Financial Studies (CFS).
  2. 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.
  3. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2006. "Nonparametric Density Estimation for Positive Time Series," Cahiers de recherche 06-09, HEC Montréal, Institut d'économie appliquée.
  4. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
  5. Matthias Hagmann & Olivier Scaillet, 2004. "Local Multiplicative Bias Correction For Asymmetric Kernel Density Estimators," Royal Economic Society Annual Conference 2004 25, Royal Economic Society.
  6. 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.
  7. Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika, Springer, vol. 76(3), pages 357-379, April.
  8. 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.
  9. 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.

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