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Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels

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  • Olivier SCAILLET

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

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.

Suggested Citation

  • Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," LIDAM Discussion Papers IRES 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2001017
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    1. Jones, Larry E & Manuelli, Rodolfo E, 1992. "The Coordination Problem and Equilibrium Theories of Recessions," American Economic Review, American Economic Association, vol. 82(3), pages 451-471, June.
    2. Jacques Drèze, 2001. "On the Macroeconomics of Uncertainty and Incomplete Markets," International Economic Association Series, in: Jacques Drèze (ed.), Advances in Macroeconomic Theory, chapter 3, pages 30-55, Palgrave Macmillan.
    3. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 441-463.
    4. Gali, Jordi, 1996. "Multiple Equilibria in a Growth Model with Monopolistic Competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 251-266, August.
    5. Dreze, Jacques H., 1997. "Walras--Keynes equilibria coordination and macroeconomics," European Economic Review, Elsevier, vol. 41(9), pages 1735-1762, December.
    6. Nobuhiro Kiyotaki, 1988. "Multiple Expectational Equilibria Under Monopolistic Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(4), pages 695-713.
    7. Oliver Hart, 1982. "A Model of Imperfect Competition with Keynesian Features," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(1), pages 109-138.
    8. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    9. Roberts, John, 1987. "An Equilibrium Model with Involuntary Unemployment at Flexible, Competitive Prices and Wages," American Economic Review, American Economic Association, vol. 77(5), pages 856-874, December.
    10. John Bryant, 1983. "A Simple Rational Expectations Keynes-type Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(3), pages 525-528.
    11. Howitt, Peter & McAfee, R Preston, 1992. "Animal Spirits," American Economic Review, American Economic Association, vol. 82(3), pages 493-507, June.
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    Cited by:

    1. 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.
    2. 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.
    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.
    4. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    5. 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.
    6. 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.
    7. 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.
    8. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.

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    More about this item

    Keywords

    Boundary bias; Inverse Gaussian kernel; Reciprocal inverse Gaussian kernel; Gamma kernel; Variable kernel; Density estimation;
    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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