Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 43, 2024 - Issue 2
54
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Constrained Bayesian method for testing composite hypotheses concerning normal distribution with equal parameters

ORCID Icon, &
Pages 147-178 | Received 31 Mar 2023, Accepted 26 Feb 2024, Published online: 16 May 2024

REFERENCES

  • Abdel-Aty, S. 1954. “Approximate Formulae for the Percentage Points and the Probability Integral of the Non-Central χ2 Distribution.” Biometrika 41 (3/4): 538–540. https://doi.org/10.2307/2332731.
  • Andersson, S. 1982. “Distributions of Maximal Invariants Using Quotient Measures.” The Annals of Statistics 10 (3): 955–961. https://doi.org/10.1214/aos/1176345885.
  • Benjamini, Y., Y. Hochberg, and Y. Kling. 1993. “False Discovery Rate Control in Pairwise Comparisons.” Working Paper 93-2, Department of Statistics and Operations Research, Tel Aviv University.
  • Benjamini, Y., and D. Yekutieli. 2005. “False Discovery Rate–Adjusted Multiple Confidence Intervals for Selected Parameters.” Journal of the American Statistical Association 100 (469): 71–81. https://doi.org/10.1198/016214504000001907.
  • Bhattacharjee, D., and N. Mukhopadhyay. 2011. “On MP Test and MVUEs in a N(θ,cθ) Distribution with Unknown θ: Illustrations and Applications.” Journal of the Japan Statistical Society 41: 75–91.
  • Bhattacharjee, D., and N. Mukhopadhyay. 2012. “On SPRT and RSPRT for the Unknown Mean in a Normal Distribution with Equal Mean and Variance.” Sequential Analysis 31 (1): 108–134. https://doi.org/10.1080/07474946.2012.652015.
  • Bhattacharjee, D., and N. Mukhopadhyay. 2015. “Confidence Interval Estimation Following SPRT in a Normal Distribution with Equal Mean and Variance.” Sequential Analysis 34 (4): 504–531. https://doi.org/10.1080/07474946.2015.1099948.
  • Johnson, N. L., S. Kotz, and N. Balakrishnan. 2004. Continuous Univariate Distributions. Vol. 2. New York: Wiley.
  • Jones, L. V., and J. W. Tukey. 2000. “A Sensible Formulation of the Significance Test.” Psychological Methods 5 (4): 411–414. https://doi.org/10.1037/1082-989x.5.4.411.
  • Kachiashvili, K. J. 2016. “Constrained Bayesian Method of Composite Hypotheses Testing: Singularities and Capabilities.” International Journal of Statistics in Medical Research 5 (3): 135–167. https://doi.org/10.6000/1929-6029.2016.05.03.1.
  • Kachiashvili, K. J. 2018. Constrained Bayesian Methods of Hypotheses Testing: A New Philosophy of Hypotheses Testing in Parallel and Sequential Experiments. New York: Nova Science Publishers.
  • Kachiashvili, K. J., and A. Mueed. 2013. “Conditional Bayesian Task of Testing Many Hypotheses.” Statistics 47 (2): 274–293. https://doi.org/10.1080/02331888.2011.602681.
  • Kachiashvili, K. J., J. K. Kachiashvili, and I. A. Prangishvili. 2020. “CBM for Testing Multiple Hypotheses with Directional Alternatives in Sequential Experiments.” Sequential Analysis 39 (1): 115–131. https://doi.org/10.1080/07474946.2020.1727166.
  • Kachiashvili, K. J., M. A. Hashmi, and A. Mueed. 2012. “Sensitivity Analysis of Classical and Conditional Bayesian Problems of Many Hypotheses Testing.” Communications in Statistics—Theory and Methods 41 (4): 591–605. https://doi.org/10.1080/03610926.2010.510255.
  • Kaiser, H. F. 1960. “Directional Statistical Decisions.” Psychological Review 67 (3): 160–167. https://doi.org/10.1037/h0047595.
  • Karlin, S., and H. Rubin. 1956. “The Theory of Decision Procedures for Distributions in Monotone Likelihood Ratio.” The Annals of Mathematical Statistics 27 (2): 272–299. https://doi.org/10.1214/aoms/1177728259.
  • Marchand, E. 1996. “Computing the Moments of a Truncated Noncentral Chi-Square Distribution.” Journal of Statistical Computation and Simulation 54 (4): 387–391. https://doi.org/10.1080/00949659608811742.
  • Mukhopadhyay, N., and G. Cicconetti. 2004. “Applications of Sequentially Estimating the Mean in a Normal Distribution Having Equal Mean and Variance.” Sequential Analysis 23 (4): 625–665. https://doi.org/10.1081/SQA-200039002.
  • Mukhopadhyay, N., and B. M. de Silva. 2008. “Theory and Applications of a New Methodology for the Random Sequential Probability Ratio Test.” Statistical Methodology 5 (5): 424–453. https://doi.org/10.1016/j.stamet.2007.10.002.
  • Mukhopadhyay, N., and C. Zhang. 2018. “EDA on the Asymptotic Normality of the Standardized Sequential Stopping Times, Part-I: Parametric Models.” Sequential Analysis 37 (3): 342–374. https://doi.org/10.1080/07474946.2018.1548847.
  • Mukhopadhyay, N., and C. Zhang. 2020. “EDA on the Asymptotic Normality of the Standardized Sequential Stopping Times, Part-II: Distribution-Free Models.” Sequential Analysis 39 (3): 367–398. https://doi.org/10.1080/07474946.2020.1823193.
  • Shaffer, J. P. 2002. “Multiplicity, Directional (Type III) Errors, and the Null Hypothesis.” Psychological Methods 7 (3): 356–369. https://doi.org/10.1037/1082-989x.7.3.356.
  • Wald, A. 1947. Sequential Analysis. New York: Wiley.
  • Wijsman, R. A. 1967. “Cross-Sections of Orbits and Their Application to Densities of Maximal Invariants.” In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, edited by Lucien M. Le Cam and Jerzy Neyman, Vol. 1, 389–400. Berkeley: University of California Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.