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Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels

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  • O. Scaillet

Abstract

This paper introduces two new nonparametric estimators for probability density functions which have support on the non-negative half-line. These kernel estimators are based on some inverse Gaussian and reciprocal inverse Gaussian probability density functions used as kernels. We show that they share the same properties as those of gamma kernel estimators : they are free of boundary bias, always non-negative, and achieve the optimal rate of convergence for the mean integrated squarred error. Extensions to regression curve estimation and hazard rate estimation under random censoring are briefly discussed. Monte Carlo results concerning finite sample properties are reported for different distributions.
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Suggested Citation

  • O. Scaillet, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels," Thema Working Papers 2001-24, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:2001-24
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    Cited by:

    1. 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.
    2. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    3. 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.
    4. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    5. Kapetanios, George, 2008. "Bootstrap-based tests for deterministic time-varying coefficients in regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 534-545, December.
    6. Xiaodong Jin & Janusz Kawczak, 2003. "Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 103-124, May.
    7. George Kapetanios, 2005. "Tests for Deterministic Parametric Structural Change in Regression Models," Working Papers 539, Queen Mary University of London, School of Economics and Finance.
    8. Muhammad Hanif, 2011. "Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels," Far East Journal of Psychology and Business, Far East Research Centre, vol. 4(5), pages 53-69, July.
    9. 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.
    10. N. Balakrishna & Hira L. Koul, 2017. "Varying kernel marginal density estimator for a positive time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 531-552, July.
    11. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    12. Ané, Thierry & Métais, Carole, 2009. "The distribution of realized variances: Marginal behaviors, asymmetric dependence and contagion effects," International Review of Financial Analysis, Elsevier, vol. 18(3), pages 134-150, June.
    13. 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.
    14. 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.
    15. 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.
    16. Eduardo Fé, 2010. "An application of local linear regression with asymmetric kernels to regression discontinuity designs," Economics Discussion Paper Series 1016, Economics, The University of Manchester.

    More about this item

    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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