Browse > Article

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)
Publication Information
Journal of the Korean Statistical Society / v.34, no.3, 2005 , pp. 245-261 More about this Journal
Abstract
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.
Keywords
Truncated bivariate t; Skew-t distribution; Bayesian method; Markov chain Monte Carlo method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 ARNOLD, B. C., CASTILLO, A. AND SARABIA, J. M. (2002). 'Conditionally specified multivariate skew distributions', Sankhya, A64, 206-226
2 BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed., New York: Springer-Verlag
3 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   DOI   ScienceOn
4 GELMAN, A., CARLIN, J. B., STERN, H. S., AND RUBIN, D. B. (2000). Bayesian Data Analysis, New York: Chapman and Hall
5 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
6 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   DOI   ScienceOn
7 KIM, H. J. (2002). 'Binary regression with a class of skewed t link models', Communications in Statistics- Theory and Methods, 31, 1863-1886   DOI   ScienceOn
8 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   DOI   ScienceOn
9 HENZE, N. (1986). 'A probabilistic representation of the skew-normal distribution', Scandinavian Journal of Statistics, 13, 271-275
10 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   DOI   ScienceOn
11 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
12 BRANCO, M. D. AND DEY, D. K. (2001). 'A general class. of multivariate skew-elliptical distributions', Journal of Multivariate Analysis, 79, 99-113   DOI   ScienceOn
13 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   DOI   ScienceOn
14 CHIB, S. AND GREENBERG, E. (1995). 'Understanding the Metropolis-Hastings Algorithm', The American Statistician, 49, 327-335   DOI   ScienceOn
15 AZZALINI, A. AND DALLA VALLE, A. (1996). 'The multivariate skew-normal distribution', Biometrika, 83, 715-726   DOI   ScienceOn
16 COWLES, M. AND CARLIN, B. (1996). 'Markov chain Monte Carlo diagnostics: A comparative review', Journal of the American Statistical Association, 91, 883-904   DOI   ScienceOn
17 LEE. P. M. (1997). Bayesian Statistics, 2nd ed., New York: John Wiley
18 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   DOI   ScienceOn
19 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   DOI   ScienceOn
20 GUSTAFSON, P. (1998). 'A guided walk Metropolis algorithm', Statistics and Computing, 8, 357-364   DOI
21 JOHNSON, N. L., KOTZ, S., AND BALAKRISHNAN, N. (1995). Continuous Univariate Distributions, Vol. 2, New York: John Wiley
22 AZZALINI, A. (1985). 'A class of distributions which includes the normal ones', Scandinavian Journal of Statistics, 12, 171-178
23 DEVROYE, L. (1986). Non-Uniform Random Variate Generation, New York: Springer Verlag
24 COHEN, A. C. (1991). Truncated and Censored Samples: Theory and Applications, New York: Marcel Dekker