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

  • Song Li

    ()

  • Mervyn J. Silvapulle

    ()

  • Param Silvapulle

    ()

  • Xibin Zhang

    ()

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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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
Contact details of provider: Postal: PO Box 11E, Monash University, Victoria 3800, Australia
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Web page: http://www.buseco.monash.edu.au/depts/ebs/
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  1. 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.
  2. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
  3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  4. 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.
  5. 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.
  6. 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.
  7. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  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. 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.
  10. Ferreira José António & Zwinderman Aeilko H, 2006. "Approximate Power and Sample Size Calculations with the Benjamini-Hochberg Method," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-38, September.
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