ESTIMATING THE SIMULTANEOUS CONFIDENCE LEVELS FOR THE DIFFERENCE OF PROPORTIONS FROM MULTIVARIATE BINOMIAL DISTRIBUTIONS

  • Published : 2007.09.30

Abstract

For the two groups data from multivariate binomial distribution, we consider a bootstrap approach to inferring the simultaneous confidence level and its standard error of a collection of the dependent confidence intervals for the difference of proportions with an experimentwise error rate at the a level are presented. The bootstrap method is used to estimate the simultaneous confidence probability for the difference of proportions.

Keywords

References

  1. BEAL, S. L. (1987). 'Asymptotic confidence intervals for the difference between two binomial parameters for use with small samples', Biometrics, 43, 941-950 https://doi.org/10.2307/2531547
  2. BICKEL, P. J. AND FREEDMAN, D. A. (1981). 'Some asymptotic theory for the bootstrap', The Annals of Statistics, 9, 1196-1217 https://doi.org/10.1214/aos/1176345637
  3. BROWN, C. C. AND FEARS, T. R. (1981). 'Exact significance levels for multiple binomial testing with application to carcinogenicity screens', Biometrics, 37, 763-774 https://doi.org/10.2307/2530158
  4. HOCHBERG, Y. (1988). 'A sharper Bonferroni procedure for multiple tests of significance', Biometrika, 75, 800-802 https://doi.org/10.1093/biomet/75.4.800
  5. HOLLAND, B. S. AND COPENHAVER, M. D. (1987). 'An improved sequentially rejective Bonferroni test procedure', Biometrics, 43, 417-423 https://doi.org/10.2307/2531823
  6. JHUN, M., JEONG, H. C. AND BAHNG, J. S. (2007). 'Simultaneous confidence intervals for the mean of multivariate poisson distribution: a comparison', Communications in Statistics-Simulation and Computation, 36, 151-164 https://doi.org/10.1080/03610910601096569
  7. MEE, R. W. (1984). 'Confidence bounds for the difference between two probabilities', Biometrics, 40, 1175-1176
  8. MIETTINEN, O. AND NURMINEN, M. (1985). 'Comparative analysis of two rates', Statistics in Medicine, 4, 213-226 https://doi.org/10.1002/sim.4780040211
  9. NEWCOMBE, R. G. (1998). 'Interval estimation for the difference between independent proportions: comparison of eleven methods', Statistics in Medicine, 17, 873-890 https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I
  10. PARK, C. G., PARK, T. S. AND SHIN, D. W. (1996). 'A simple method for generating correlated binary variates', The American Statistician, 50, 306-310 https://doi.org/10.2307/2684925
  11. SANTNER, T. J. AND SNELL, M. K. (1980). 'Small-sample confidence intervals for PI - P2 and pl/P2 in 2 x 2 contingency tables', Journal of the American Statistical Association, 75, 386-394 https://doi.org/10.2307/2287464
  12. SINGH, K. (1981). 'On the asymptotic accuracy of Efron's bootstrap', The Annals of Statistics, 9, 1187-1195 https://doi.org/10.1214/aos/1176345636
  13. WESTFALL, P. (1985). 'Simultaneous small-sample multivariate Bernoulli confidence intervals', Biometrics, 41, 1001-1013 https://doi.org/10.2307/2530971
  14. WESTFALL, P. H. AND YOUNG, S. S. (1989). 'p-value adjustments for multiple tests in multivariate binomial models', Journal of the American Statistical Association, 84, 780-786 https://doi.org/10.2307/2289666
  15. WESTFALL, P. H. AND YOUNG, S. S. (1993). Resampling-Based Multiple Testing: Examples and Methods for p- Value Adjustment, John Wiley & Sons, New York