• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.257-266
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• 2007

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.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.445-455
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• 2011

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.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.275-284
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• 2007

Confidence intervals for the population proportion in a double sampling scheme subject to false-positive misclassification are considered. The confidence intervals are obtained by applying Agresti and Coull's approach, so-called "adding two-failures and two successes". They are compared in terms of coverage probabilities and expected widths with the Wald interval and the confidence interval given by Boese et al. (2006). The latter one is a test-based confidence interval and is known to have good properties. It is shown that the Agresti and Coull's approach provides a relatively simple but effective confidence interval.

• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.607-615
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• 2005

Recently the interval estimation of a binomial proportion is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the will-known Wald confidence interval. Various alternatives have been proposed. Among them, Agresti-Coull confidence interval has been recommended by Brown et al. (2001) with other confidence intervals for large sample, say n $\ge$ 40. On the other hand, a noninformative Bayesian approach called Polya posterior often produces statistics with good frequentist's properties. In this note, an interval estimator is developed using weighted Polya posterior. The resulting interval estimator is essentially the Agresti-Coull confidence interval with some improved features. It is shown that the weighted Polys posterior produce an effective interval estimator for small sample size and a severely skewed binomial distribution.

• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1289-1300
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• 2009

The double sampling scheme is effective in reducing the sampling cost. However, the doubly sampled data is contaminated by two types of error, namely false-positive and false-negative errors. These would make the statistical analysis more difficult, and it would require more sophisticate analysis tools. For instance, the Wald method for the interval estimation of a proportion would not work well. In fact, it is well known that the Wald confidence interval behaves very poorly in many sampling schemes. In this note, the property of the Wald interval is investigated in terms of the coverage probability and the expected width. An alternative confidence interval based on the Agresti-Coull's approach is recommended.