Logarithmic confidence intervals for the cross-product ratio of binomial proportions under different sampling schemes

References

• Albert, J. H., and A. K. Gupta. 1983. Estimation in contingency tables using prior information. Journal of the Royal Statistical Society. Series B (Methodological) 45:60–69. doi:10.1111/j.2517-6161.1983.tb01231.x.
   Google Scholar
• Amini, M., and M. Mahdizadeh. 2017. Nonparametric estimation of the entropy using a ranked set sample. Communications in Statistics – Simulation and Computation 46:6719–37. doi:10.1080/03610918.2016.1208229.
   Web of Science ®Google Scholar
• Andĕl, J. 1973. On interactions in contingency tables. Aplikace Matematiky 18:99–109.
   Google Scholar
• Baxter, P. D., and P. R. Marchant. 2010. The cross-product ratio in bivariate lognormal and gamma distributions, with an application to non-randomized trials. Journal of Applied Statistics 37 (4):529–36. doi:10.1080/02664760902744962.
   Web of Science ®Google Scholar
• Cornfield, J. 1956. A statistical problem arising from retrospective studies. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Vol. 4. Berkeley, CA: University of California Press,
   Google Scholar
• Gart, J. J. 1962. On the combination of relative risks. Biometrics 18 (4):601–10. doi:10.2307/2527905.
   Web of Science ®Google Scholar
• Goodman, L. A. 1964. Simultaneous confidence limits for cross-product ratios in contingency tables. Journal of the Royal Statistical Society. Series B (Methodological) 26:86–102. doi:10.1111/j.2517-6161.1964.tb00543.x.
   Web of Science ®Google Scholar
• Holland, P. W., and Y. J. Wang. 1987. Dependence functions for Continuous bivariate densities. Communications in Statistics – Theory and Methods 16:863–76. doi:10.1080/03610928708829408.
   Web of Science ®Google Scholar
• Lee, L.-F. 1981. Empirical Bayes estimators for the cross-product ratios for 2 × 2 contingency tables. Ph.D.thesis, Virginia Polytechnic Institute and State University.
   Google Scholar
• Lehmann, E. L. 1997. Elements of large sample theory. New York: Springer-Verlag.
   Google Scholar
• Lin, C.-Y., and M.-C. Yang. 2008. Improved p-value tests for comparing two independent binomial proportions. Communications in Statistics – Simulation and Computation 38:78–91. doi:10.1080/03610910802417812.
   Web of Science ®Google Scholar
• Mahdizadeh, M., and N. R. Arghami. 2012. Quantile estimation using ranked set samples from a population with known mean. Communications in Statistics – Simulation and Computation 41:1872–81. doi:10.1080/03610918.2011.624236.
   Web of Science ®Google Scholar
• Martín Andrés, A., J. M. Tapia García, and F. Gayá Moreno. 2020. Two-tailed asymptotic inferences for the odds ratio in cross-sectional studies: Evaluation of fifteen old and new methods of inference. Journal of Biopharmaceutical Statistics 30:900–915.
   PubMed Web of Science ®Google Scholar
• McCann, M. H., and J. M. Tebbs. 2009. Simultaneous logit-based confidence intervals for odds ratios in 2×k classification tables with a fixed reference level. Communications in Statistics – Simulation and Computation 38:961–75.
   Web of Science ®Google Scholar
• Ngamkham, T. 2018. Confidence interval estimation for the ratio of binomial proportions and random numbers generation for some statistical models. Ph. D. thesis, University of Regina.
   Google Scholar
• Ngamkham, T., A. Volodin, and I. Volodin. 2016. Confidence intervals for a ratio of binomial proportions based on direct and inverse sampling schemes. Lobachevskii Journal of Mathematics 37 (4):466–96. doi:10.1134/S1995080216040132.
   Web of Science ®Google Scholar
• Niebuhr, T., and M. Trabs. 2019. Profiting from correlations: Adjusted estimators for categorical data. Applied Stochastic Models in Business and Industry 35 (4):1090–102. doi:10.1002/asmb.2452.
   Web of Science ®Google Scholar
• Schaarschmidt, F., D. Gerhard, and C. Vogel. 2017. Simultaneous confidence intervals for comparisons of several multinomial samples. Computational Statistics and Data Analysis 106:65–76. doi:10.1016/j.csda.2016.09.004.
   Web of Science ®Google Scholar
• Sungboonchoo, C., T. Ngamkham, W. Panichkitkosolkul, and A. Volodin. 2021. Confidence estimation of the cross-product ratio of binomial proportions under different sampling schemes. Lobachevskii Journal of Mathematics 42 (2):1–16.
   Web of Science ®Google Scholar
• Wang, Y. J. 1987. The probability integrals of bivariate normal distributions: A contingency table approach. Biometrika 74:185–90. doi:10.1093/biomet/74.1.185.
   Web of Science ®Google Scholar
• Xu, J. L. 2012. A property of the generalized proportional hazards model. Far East Journal of Theoretical Statisitcs 41 (2):149–62.
   Google Scholar