The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Confidence Intervals for a Linear Function of Binomial Proportions Based on a Bayesian Approach

베이지안 접근에 의한 모비율 선형함수의 신뢰구간

  • 이승천 (한신대학교 정보통계학과)
  • Published : 2007.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

It is known that Agresti-Coull approach is an effective tool for the construction of confidence intervals for various problems related to binomial proportions. However, the Agrest-Coull approach often produces a conservative confidence interval. In this note, confidence intervals based on a Bayesian approach are proposed for a linear function of independent binomial proportions. It is shown that the Bayesian confidence interval slightly outperforms the confidence interval based on Agresti-Coull approach in average sense.

모비율에 대한 신뢰구간의 구축에 있어 정규근사에 의한 Wald 신뢰구간이 표준으로 인식되어 왔으나, 최근 여러 학자들에 의해 Wald 신뢰구간은 근사성에서 심각한 문제가 있다는 것이 밝혀지고 있어 Agresti와 Coull(1998)에 의해 제안된 방법이 새로운 표준이 되어 가고 있다. Agresti-Coull 방법은 간편하면서도 근사성 문제를 획기적으로 개선하였으나 모비율에 대한 여러 가지 문제에서 보수적인 신뢰구간을 제시하고 있다. 본 연구에서는 베이지안 접근 방법에 의해 Agresti-Coull 방법의 보수성을 개선한 모비율 선형 함수의 신뢰구간을 제시한다.

Keywords

References

  1. 이승천 (2005). 이항비율의 가중 Polys posterior 구간추정, <응용통계 연구>, 18, 607-615 https://doi.org/10.5351/KJAS.2005.18.3.607
  2. 이승천 (2006). 독립표본에서 두 모비율의 차이에 대한 가중 Polya 사후분포 신뢰구간, <응용통계연구>, 19, 171-181 https://doi.org/10.5351/KJAS.2006.19.1.171
  3. Agresti, A. and Coull, B. A. (1998). Approximation is better than 'exact' for interval estimation of binomial proportions, The American Statistician, 52, 119-126 https://doi.org/10.2307/2685469
  4. Agresti, A. and Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures, The American Statistician, 54, 280-288 https://doi.org/10.2307/2685779
  5. Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions, Statistics in Medicine, 24, 729-740 https://doi.org/10.1002/sim.1781
  6. Anbar, D. (1983). On estimating the difference between two probabilities, with special reference to clinical trials, Biometrics, 39, 257-262 https://doi.org/10.2307/2530826
  7. 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
  8. 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
  9. Bonett, D. G. and Woodward, J. A. (1987). Application of Kronecker product and Wald test in log-linear models, Computational Statistics, 3, 235-243
  10. Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101-133
  11. Brown, L. D., Cai, T. T. and DasGupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions, Annals of Statistics, 30. 160-201 https://doi.org/10.1214/aos/1015362189
  12. Ghosh, B. K. (1979). A comparison of some approximate confidence intervals for the binomial parameter, Journal of the American Statistical Association, 74, 894-900 https://doi.org/10.2307/2286420
  13. Greenland, S. (2001). Simple and effective confidence intervals for proportions and difference of proportions result from adding two successes and two failures, The American Statistician, 55, 172
  14. Lee, S.-C. (2007). An improved confidence interval for the population proportion in a double sampling scheme subject to false-positive misclassification, Journal of Korean Statistical Society, 36, 275-284
  15. Newcombe, R. (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
  16. Price, R. M. and Bonett, D. G. (2004). An improved confidence interval for a linear function of binomial proportions, Computational Statistics & Data Analysis, 45, 449-456 https://doi.org/10.1016/S0167-9473(03)00007-0

Cited by

  1. A Bayesian approach to obtain confidence intervals for binomial proportion in a double sampling scheme subject to false-positive misclassification vol.37, pp.4, 2008, https://doi.org/10.1016/j.jkss.2008.05.001