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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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Bibliographic Info

Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2001-24.

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Date of creation: 2001
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Handle: RePEc:ema:worpap:2001-24

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  1. Hart, Oliver, 1982. "A Model of Imperfect Competition with Keynesian Features," The Quarterly Journal of Economics, MIT Press, vol. 97(1), pages 109-38, February.
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  6. Jacques H.DREZE, 2001. "On the Macroeconomics of Uncertainty and Incomplete Markets," Discussion Papers (REL - Recherches Economiques de Louvain) 2001011, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Gali, Jordi, 1996. "Multiple Equilibria in a Growth Model with Monopolistic Competition," Economic Theory, Springer, vol. 8(2), pages 251-66, August.
  8. 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 451-71, June.
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Cited by:
  1. Fe, Eduardo, 2012. "Efficient estimation in regression discontinuity designs via asymmetric kernels," MPRA Paper 38164, University Library of Munich, Germany.
  2. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Nonparametric density estimation for positive time series," CORE Discussion Papers 2006085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. 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.
  5. 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.
  6. Marcelo Fernandes & Joachim Grammig, 2000. "Non-Parametric Specification Tests For Conditional Duration Models," Computing in Economics and Finance 2000 40, Society for Computational Economics.
  7. 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.
  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. 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.
  10. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
  11. 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.

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