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Bayesian Approaches to Non-parametric Estimation of Densities on the Unit Interval

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  • Song Li

    ()

  • Mervyn J. Silvapulle

    ()

  • Param Silvapulle

    ()

  • Xibin Zhang

    ()

Abstract

This paper investigates nonparametric estimation of density on [0,1]. The kernel estimator of density on [0,1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0,1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0,1] are presently estimated.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2012/wp3-12.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 3/12.

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Length: 31 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:msh:ebswps:2012-3

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Related research

Keywords: Asymmetric kernel; Bayes factor; boundary bias; kernel selection; marginal likelihood; recovery-rate density;

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  1. DiRienzo A. G., 2006. "The Two Sample Problem for Multiple Categorical Variables," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-24, July.
  2. Y.K. Tse & Xibin Zhang & Jun Yu, 2002. "Estimation of Hyperbolic Diffusion Using MCMC Method," Monash Econometrics and Business Statistics Working Papers 18/02, Monash University, Department of Econometrics and Business Statistics.
  3. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
  4. Joachim Grammig & Michael Melvin & Christian Schlag, 2005. "Internationally Cross-Listed Stock Prices During Overlapping Trading Hours: Price Discovery and Exchange Rate Effects," Working Paper Series: Finance and Accounting 78, Department of Finance, Goethe University Frankfurt am Main.
  5. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor and Francis Journals, vol. 4(2), pages 158-169.
  6. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
  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. Calabrese, Raffaella & Zenga, Michele, 2010. "Bank loan recovery rates: Measuring and nonparametric density estimation," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 903-911, May.
  9. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  10. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
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