Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 978691, 5 pages
http://dx.doi.org/10.1155/2014/978691
Research Article

Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

School of Economics, Beijing Technology and Business University, Beijing 100048, China

Received 13 October 2013; Accepted 28 January 2014; Published 4 March 2014

Academic Editor: Francis T. K. Au

Copyright © 2014 Yuliang Yin and Baoren Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K.-W. Tsui and S. Weerahandi, “Generalized P-values in significance testing of hypotheses in the presence of nuisance parameters,” Journal of the American Statistical Association, vol. 84, no. 406, pp. 602–607, 1989. View at Google Scholar · View at MathSciNet
  2. H. Jeffreys, Theory of Probability, Oxford University Press, 3rd edition, 1967.
  3. D. L. Wallace, The Behrens-Fisher and Feiller-Creasy Problems, Edited by R. A. Fisher, Springer, New York, NY, USA, 1980. View at MathSciNet
  4. X.-L. Meng, “Posterior predictive P-values,” The Annals of Statistics, vol. 22, no. 3, pp. 1142–1160, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  5. B. V. Behrens, “Ein Beitrag zur Fehlerberechnung bei wenige Beobachtungen,” Landwirtschaftliches Jahresbuch, vol. 68, pp. 807–837, 1929. View at Google Scholar
  6. M. S. Bartlett, “The information available in small samples,” Proceedings of the Cambridge Philosophical Society, vol. 32, no. 4, pp. 560–566, 1936. View at Publisher · View at Google Scholar
  7. R. A. Fisher, “The fiducial argument in statistical inference,” The Annals of Eugenics, vol. 11, pp. 141–172, 1935. View at Google Scholar
  8. B. L. Welch, “The significance of the difference between two means when the population variances are unequal,” Biometrika, vol. 29, pp. 350–362, 1938. View at Google Scholar
  9. B. L. Welch, “The generalization of student's problem when several different population variances are involved,” Biometrika, vol. 34, pp. 28–35, 1947. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Jeffreys, Theory of Probability, Oxford University Press, 1961. View at MathSciNet
  11. S. S. Wilks, “On the problem of two samples from normal populations with unequal variances,” Annals of Mathematical Statistics, vol. 11, no. 4, pp. 475–476, 1940. View at Publisher · View at Google Scholar
  12. H. Chernoff, “Asymptotic studentization in testing of hypotheses,” Annals of Mathematical Statistics, vol. 20, pp. 268–278, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. U. Chand, “Distributions related to comparison of two means and two regression coefficients,” Annals of Mathematical Statistics, vol. 21, pp. 507–522, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. K. Banerjee, “Approximate confidence interval for linear functions of means of k populations when the population variances are not equal,” Sankhya, vol. 22, pp. 357–358, 1960. View at Google Scholar · View at MathSciNet
  15. M. S. Srivastava, “On a sequential analogue of the Behrens-Fisher problem,” Journal of the Royal Statistical Society B, vol. 32, pp. 144–148, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Ghosh and Y. Kim, “The Behrens-Fisher problem revisited: a Bayes-frequentist synthesis,” Biometrika, vol. 29, no. 1, pp. 5–17, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. R. Madruga, C. A. B. Pereira, and J. M. Stern, “Bayesian evidence test for precise hypotheses,” Journal of Statistical Planning and Inference, vol. 117, no. 2, pp. 185–198, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. T. L. McMurry, D. N. Politis, and J. P. Romano, “Subsampling inference with K populations and a non-standard Behrens-Fisher problem,” International Statistical Review, vol. 80, no. 1, pp. 149–175, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Y. Yin, “A new Bayesian procedure for testing point null hypotheses,” Computational Statistics, vol. 27, no. 2, pp. 237–249, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. D. V. Lindley, “A statistical paradox,” Biometrika, vol. 44, pp. 187–192, 1957. View at Google Scholar
  21. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, San Francisco, Calif, USA, 1975.
  22. J. K. Ghosh, M. Delampady, and T. Samanta, An Introduction to Bayesian Analysis, Springer, New York, NY, USA, 2006. View at MathSciNet