DOI QR코드

DOI QR Code

Confidence Intervals for a Proportion in Finite Population Sampling

Lee, Seung-Chun

  • 발행 : 2009.05.31

초록

Recently the interval estimation of binomial proportions is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the well-known Wald confidence interval. Various alternatives have been proposed. Among them, the Agresti-Coull confidence interval, the Wilson confidence interval and the Bayes confidence interval resulting from the noninformative Jefferys prior were recommended by Brown et al. (2001). However, unlike the binomial distribution case, little is known about the properties of the confidence intervals in finite population sampling. In this note, the property of confidence intervals is investigated in anile population sampling.

키워드

Wald interval;Agresti-Coull interval;Wilson interval;Weighted Polya posterior interval;exact interval;combined interval;hypergeometric distribution

참고문헌

  1. Agresti, A. and Coull, B. A. (1998). Approximation is better than 'exact' for interval estimation of binomial proportions, American Statistician, 52, 119-126 https://doi.org/10.2307/2685469
  2. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, Springer, New York
  3. Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108-116 https://doi.org/10.2307/2287116
  4. Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101-133
  5. Brown, L. D., Cai, T. T. and DasGupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions, The Annals of Statistics, 30, 160-201 https://doi.org/10.1214/aos/1015362189
  6. Casella, G. T., Hwang, T. G. and Robert, C. P. (1994). Loss functions for set estimation, Statistical Decision Theory and Related Topics V (Edited by S. S. Gupta and J. O. Berger), Springer-Verlag
  7. Cai, Y. and Krishnamoorthy, K. (2005). A simple improved inference methods for some discrete distributions, Computational Statistics & Data Analysis, 48, 605-621 https://doi.org/10.1016/j.csda.2004.03.008
  8. Clopper, C. J. and Pearson, E. S. (1936). The use of confidence or fiducial limits illustrated in the case of binomial, Biometriks, 26, 404-413 https://doi.org/10.1093/biomet/26.4.404
  9. Chocran, W. G. (1977). Sampling Techniques, 3rd ed. Wiley, New York
  10. Esty, W. E. and Banfield, J. D. (2003). The box-percentile plot, Journal of Statistical Software, 8, Issue 17
  11. Krishnamoorthy, K., Thomson, J. and Cai, Y. (2004), An exact method of testing equality of several binomial proportions to a specified standard, Computational Statistics & Data Analysis, 45, 697-707 https://doi.org/10.1016/S0167-9473(03)00095-1
  12. Kulkarni, P. M. and Shah, A. K. (1995). Testing the equality of several binomial proportions to prespecifled standard, Statistic & Probability Letter, 25, 213-219 https://doi.org/10.1016/0167-7152(94)00224-V
  13. Lee, S.-C. (2005). Interval estimation of binomial proportions based on weighted Polya posterior, Computational Statistics & Data Analysis, 51, 1012-1021 https://doi.org/10.1016/j.csda.2005.10.008
  14. Lee, S,-C. (2009). Choosing between the exact and the asymptotic confidence intervals: For the difference of two independent binomial proportions, Communications of the Korean Statistical Society, 16, 363-372 https://doi.org/10.5351/CKSS.2009.16.2.363
  15. Meeden, G. D. (1999). Interval estimators for the population mean for skewed distributions with a small sample size, Journal of Applied Statistics, 26, 81-96 https://doi.org/10.1080/02664769922674
  16. Staner, T. J. (1998). A note on teaching binomial confidence intervals, Teaching Statistics, 20, 20-23 https://doi.org/10.1111/j.1467-9639.1998.tb00753.x
  17. Wilson, E. B. (1927). Probable inference, the law of succession and statistical inference, Journal of the American Statistical Association, 22, 209-212 https://doi.org/10.2307/2276774
  18. Yamane, T. (1967). Elementary Sampling Theory, Prentice-Hall Inc., Englewood Cliffs, New York