Journal of the Korean Statistical Society

  • 제34권3호
  • /
  • Pages.245-261
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  • 2005
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  • 1226-3192(pISSN)
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  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

ON BAYESIAN ESTIMATION AND PROPERTIES OF THE MARGINAL DISTRIBUTION OF A TRUNCATED BIVARIATE t-DISTRIBUTION

  • KIM HEA-JUNG (Department of Statistics, Dongguk University) ;
  • KIM Ju SUNG (Department of Statistics, Dongguk University)
  • 발행 : 2005.09.01
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초록

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

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참고문헌

  1. ARNOLD, B. C., BEAVER, R. J., GROENEVELD, R. A., AND MEEKER, W. Q. (1993). 'The nontruncated marginal of a truncated bivariate normal distribution' , Psychometrica, 58, 471-478 https://doi.org/10.1007/BF02294652
  2. ARNOLD, B. C., CASTILLO, A. AND SARABIA, J. M. (2002). 'Conditionally specified multivariate skew distributions', Sankhya, A64, 206-226
  3. AZZALINI, A. (1985). 'A class of distributions which includes the normal ones', Scandinavian Journal of Statistics, 12, 171-178
  4. AZZALINI, A. AND CAPITANIO, A. (2003). 'Distributions generated by perturbation of symmetry with emphasis on a multivariate distribution', Journal of the Royal Statistical Society, B35, 367-389 https://doi.org/10.1111/1467-9868.00391
  5. AZZALINI, A. AND DALLA VALLE, A. (1996). 'The multivariate skew-normal distribution', Biometrika, 83, 715-726 https://doi.org/10.1093/biomet/83.4.715
  6. BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed., New York: Springer-Verlag
  7. BRANCO, M. D. AND DEY, D. K. (2001). 'A general class. of multivariate skew-elliptical distributions', Journal of Multivariate Analysis, 79, 99-113 https://doi.org/10.1006/jmva.2000.1960
  8. CHEN, M. H., DEY, D. K., AND SHAO, Q. M. (1999). 'A new skewed link model for dichotomous quantal response data', Journal of the American Statistical Association, 94, 1172-1185 https://doi.org/10.2307/2669933
  9. CHIB, S. AND GREENBERG, E. (1995). 'Understanding the Metropolis-Hastings Algorithm', The American Statistician, 49, 327-335 https://doi.org/10.2307/2684568
  10. COHEN, A. C. (1991). Truncated and Censored Samples: Theory and Applications, New York: Marcel Dekker
  11. COWLES, M. AND CARLIN, B. (1996). 'Markov chain Monte Carlo diagnostics: A comparative review', Journal of the American Statistical Association, 91, 883-904 https://doi.org/10.2307/2291683
  12. DEVROYE, L. (1986). Non-Uniform Random Variate Generation, New York: Springer Verlag
  13. GELFAND, A. E. AND SMITH, A. F. M. (1990). 'Sampling-based approaches to calculating marginal densities', Journal of the American Statistical Association, 85, 398-409 https://doi.org/10.2307/2289776
  14. GELFAND, A. E., SMITH, A. F. M., AND LEE, T. M. (1992). 'Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling', Journal of the American Statistical Association, 87, 523-532 https://doi.org/10.2307/2290286
  15. GELMAN, A., CARLIN, J. B., STERN, H. S., AND RUBIN, D. B. (2000). Bayesian Data Analysis, New York: Chapman and Hall
  16. GELMAN, A. ROBERT, G. 0., AND GILKS, W. R. (1996). 'Efficient Metropolis jumping rules', in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford UK: Oxford University Press, 599-607
  17. GEMAN, S. AND GEMAN, D. (1984). 'Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images', IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6, 721-741 https://doi.org/10.1109/TPAMI.1984.4767596
  18. GUSTAFSON, P. (1998). 'A guided walk Metropolis algorithm', Statistics and Computing, 8, 357-364 https://doi.org/10.1023/A:1008880707168
  19. HENZE, N. (1986). 'A probabilistic representation of the skew-normal distribution', Scandinavian Journal of Statistics, 13, 271-275
  20. JOHNSON, N. L., KOTZ, S., AND BALAKRISHNAN, N. (1995). Continuous Univariate Distributions, Vol. 2, New York: John Wiley
  21. KIM, H. J. (2002). 'Binary regression with a class of skewed t link models', Communications in Statistics- Theory and Methods, 31, 1863-1886 https://doi.org/10.1081/STA-120014917
  22. LEE. P. M. (1997). Bayesian Statistics, 2nd ed., New York: John Wiley
  23. MA, T. AND GENTON, M. G. (2004). 'A flexible class of skew-symmetric distributions. To appear in Scandinavian Journal of Statistics. http:www4.stat.ncsu.edu/mggenton/publicatiQns.html
  24. ROBERT, G. O., GELMAN, A., AND GILKS, W. R. (1997). 'Weak convergence and optimal scaling of random walk Metropolis algorithm, Annals of Applied Probability, 7, 110-120 https://doi.org/10.1214/aoap/1034625254