Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
권호 표지

Default Bayesian testing for normal mean with known coefficient of variation

  • Kang, Sang-Gil (Department of Data Information, Sangji University) ;
  • Kim, Dal-Ho (Department of Statistics, Kyungpook National University) ;
  • Le, Woo-Dong (Department of Asset Management, Daegu Haany University)
  • 투고 : 2009.12.27
  • 심사 : 2010.03.10
  • 발행 : 2010.03.31
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초록

This article deals with the problem of testing mean when the coefficient of variation in normal distribution is known. We propose Bayesian hypothesis testing procedures for the normal mean under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Specially, we develop intrinsic priors which give asymptotically same Bayes factor with the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

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참고문헌

  1. Arnholt, A. T and Hebert, J. L. (1995). Estimating the mean with known coecient of variation. The American Statistician, 49, 367-369. https://doi.org/10.2307/2684576
  2. Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means: Bayesian analysis with reference priors. Journal of the American Statistical Association, 84, 200-207. https://doi.org/10.2307/2289864
  3. Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). Bayesian Statistics IV, Oxford University Press, Oxford, 35-60.
  4. Berger, J. O. and Pericchi, L. R. (1996). The intrinsic bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122. https://doi.org/10.2307/2291387
  5. Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable bayesian model selection: The median intrinsic bayes factor. Sankya B, 60, 1-18.
  6. Berger, J. O. and Pericchi, L. R. (2001). Objective bayesian methods for model selection: Introduction and comparison (with discussion). Institute of Mathematical Statistics Lecture Notes-Monograph Series, 38, Ed. P. Lahiri, 135-207, Beachwood Ohio.
  7. Bhat, K. and Rao, K. A. (2007). On tests for a normal mean with known coecient of variation. International Statistical Review, 75, 170-182. https://doi.org/10.1111/j.1751-5823.2007.00019.x
  8. Gleser, L. J. and Healy, J. D. (1976). Estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association, 71, 977-981. https://doi.org/10.2307/2286872
  9. Guo, H. and Pal, N. (2003). On a normal mean with known coefficient of variation. Calcutta Statistical Association Bulletin, 54, 17-30. https://doi.org/10.1177/0008068320030102
  10. Hinkley, D. V. (1977). Conditional inference about a normal mean with known coefficient of variation. Biometrika, 64, 105-108. https://doi.org/10.1093/biomet/64.1.105
  11. Kang, S. G., Kim, D. H. and Lee, W. D. (2005). Bayesian analysis for the difference of exponential means. Journal of Korean Data & Information Science Society, 16, 1067-1078.
  12. Kang, S. G., Kim, D. H. and Lee, W. D. (2006). Bayesian one-sided testing for the ratio of poisson means. Journal of Korean Data & Information Science Society, 17, 619-631.
  13. Kang, S. G., Kim, D. H. and Lee, W. D. (2007). Bayesian hypothesis testing for homogeneity of the shape parameters in gamma populations. Journal of Korean Data & Information Science Society, 18, 1191-1203.
  14. Kang, S. G., Kim, D. H. and Lee, W. D. (2007). Bayesian hypothesis testing for the ratio of two quantiles in exponential distributions. Journal of Korean Data & Information Science Society, 18, 833-845.
  15. O'Hagan, A. (1995). Fractional bayes factors for model comparison (with discussion). Journal of Royal Statistical Society, B, 57, 99-118.
  16. O'Hagan, A. (1997). Properties of intrinsic and fractional bayes factors. Test, 6, 101-118. https://doi.org/10.1007/BF02564428
  17. Soofi, E. S. and Gokhale, D. V. (1991). Minimum discrimination information estimator of the mean with known coefficient of variation. Computational Statistics and Data Analysis, 11, 165-177. https://doi.org/10.1016/0167-9473(91)90067-C
  18. Spiegelhalter, D. J. and Smith, A. F. M. (1982). Bayes factors for linear and log-linear models with vague prior information. Journal of Royal Statistical Society, B, 44, 377-387.
  19. Wu, J. and Jiang, G. (2001). Small sample likelihood inference for the ratio of means. Computational Statistics and Data Analysis, 38, 181-190. https://doi.org/10.1016/S0167-9473(01)00025-1