Theoretical Considerations for the Agresti-Coull Type Confidence Interval in Misclassified Binary Data

Title & Authors
Theoretical Considerations for the Agresti-Coull Type Confidence Interval in Misclassified Binary Data
Lee, Seung-Chun;

Abstract
Although misclassified binary data occur frequently in practice, the statistical methodology available for the data is rather limited. In particular, the interval estimation of population proportion has relied on the classical Wald method. Recently, Lee and Choi (2009) developed a new confidence interval by applying the Agresti-Coull's approach and showed the efficiency of their proposed confidence interval numerically, but a theoretical justification has not been explored yet. Therefore, a Bayesian model for the misclassified binary data is developed to consider the Agresti-Coull confidence interval from a theoretical point of view. It is shown that the Agresti-Coull confidence interval is essentially a Bayesian confidence interval.
Keywords
Misclassified binary data;false-positive error;false-negative error;coverage probability;Agresti-Coull confidence interval;
Language
Korean
Cited by
1.
The Role of Artificial Observations in Testing for the Difference of Proportions in Misclassified Binary Data,;

응용통계연구, 2012. vol.25. 3, pp.513-520
2.
무관질문 확률화응답기법을 이용한 민감한 속성에 대한 모비율의 구간추정,강혜진;손창균;

Journal of the Korean Data Analysis Society, 2016. vol.18. 1B, pp.241-254
1.
The Role of Artificial Observations in Testing for the Difference of Proportions in Misclassified Binary Data, Korean Journal of Applied Statistics, 2012, 25, 3, 513
References
1.
이승천, 최병수(2009). 이중표본에서 모비율의 구간추정, <응용통계연구>, 22, 1289-1300.

2.
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.

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.

4.
Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions, Statistics in Medicine, 24, 729-740.

5.
Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108-116.

6.
Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101-133.

7.
Geng, Z. and Asano, C. (1989). Bayesian estimation methods for categorical data with misclassifications, Communications in Statistics, Theory and Methods, 18, 2935-2954.

8.
Lee, S.-C. (2006). Interval estimation of binomial proportions based on weighted Polya posterior, Computational Statistics & Data Analysis, 51, 1012-1021.

9.
Lee, S.-C. and Byun, J.-S. (2008). A Bayesian approach to obtain confidence intervals for binomial proportion in a double sampling scheme subject to false-positive misclassification, Journal of the Korean Statistical Society, 37, 393-403.

10.
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.

11.
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.

12.
Raats, V. M. and Moors, J. J. A. (2003). Double-checking auditors: A Bayesian approach, The Statistician, 52, 351-365.

13.
Tenenbein, A. (1970). A double sampling scheme for estimating from binomial data with misclassifications, Journal of the American Statistical Association, 65, 1350-1361.