Journal of the Korean Statistical Society

  • 제35권4호
  • /
  • Pages.419-439
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  • 2006
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  • 1226-3192(pISSN)
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  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

BAYESIAN ROBUST ANALYSIS FOR NON-NORMAL DATA BASED ON A PERTURBED-t MODEL

  • 발행 : 2006.12.31
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초록

The article develops a new class of distributions by introducing a nonnegative perturbing function to $t_\nu$ distribution having location and scale parameters. The class is obtained by using transformations and conditioning. The class strictly includes $t_\nu$ and $skew-t_\nu$ distributions. It provides yet other models useful for selection modeling and robustness analysis. Analytic forms of the densities are obtained and distributional properties are studied. These developments are followed by an easy method for estimating the distribution by using Markov chain Monte Carlo. It is shown that the method is straightforward to specify distribution ally and to implement computationally, with output readily adopted for constructing required criterion. The method is illustrated by using a simulation study.

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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', Psychometrika, 58, 471-488 https://doi.org/10.1007/BF02294652
  2. AZZALINI, A. (1985). 'A class of distributions which includes the normal ones'. Scandinavian Journal of Statistics, 12, 171-178
  3. BRANCO, M. D. AND DEY, D. K. (2001). 'A general class of multivariate skew-elliptical distributions', Journal of the Multivariate Analysis, 79, 99-113 https://doi.org/10.1006/jmva.2000.1960
  4. BAYARRI, M. J. AND DEGROOT, H. M. (1992). 'A BAD view of weighted distribution and selection models', Bayesian Statistics, Oxford University Press, Oxford
  5. CHIB, S. AND GREENBERG, E. (1995). 'Understanding the Metropolis-Hastings Algorithm', The American Statistician, 19, 327-335
  6. 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
  7. DEVROYE, L. (1986). Non-Uniform Random Variate Generator, Springer Verlag, New York
  8. DUNNETT, C. W. AND SOBEL, M. (1954). 'A bivariate generalization of Student's t-distribution, with tables for certain special cases', Biometrika, 41, 153-169 https://doi.org/10.1093/biomet/41.1-2.153
  9. FANG, K. T., KOTZ, S. AND NG, K. W. (1990). Symmetric Multivariate and Related Distributions, Chapman & Hall, New York
  10. FANG, K. T. AND ZHANG, Y. T. (1990). Generalized Multivariate Analysis, Springer-Verlag, New York
  11. GELMAN, A. ROBERT, G. O. AND GILKS, W. R. (1996). 'Efficient Metropolis jumping rules', Bayesian Statistics, Oxford University Press, Oxford
  12. GUSTAFSON, P. (1998). 'A guided walk Metropolis algorithm', Statistics and Computing, 8, 357-364 https://doi.org/10.1023/A:1008880707168
  13. HENZE, N. (1986). 'A probabilistic representation of the Skew-normal distribution', Scandinavian Journal of Statistics, 13, 271-275
  14. JOHNSON, N. L., KOTZ, S. AND BALAKRISHNAN, N. (1994). Continuous Univariate Distributions, John Wiley & Sons, New York
  15. 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
  16. KIM, H. J. (2005). 'On Bayesian estimation and properties of the marginal distribution of a truncated bivariate t-distribution', Journal of the Korean Statistical Society, 34, 245-261
  17. MA, Y., GENTON, M. G. AND TSIATIS, A. (2005). 'Locally efficient semiparametric estimators for generalized skew-elliptical distributions', Journal of the American Statistical Association, 100, 980-989 https://doi.org/10.1198/016214505000000079
  18. RAO, C. R. (1985). 'Weighted distributions arising out of methods of ascertainment: What population does a sample represent ?', A Celebration of Statistics: The ISI Centenary Volume (A. G. Atkinson and S. E. Fienberg, eds.), Springer, New York
  19. 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
  20. ZACKS, S (1981). Parametric Statistical Inference, Pergamon Press, Oxford