# Prof. Andrei Volodine學術專題演講(112/05/16)

• 2023-05-12
• 楊文敏

Department of Mathematics and Statistics, University of Regina, Canada
目：Confidence interval for a ratio of binomial proportions for dependent
populations

間：民國112516 (星期二) 下午300
點：政治大學商學院260909
要：
The issue of the success probability of Bernoulli trials lies in multiple subject fields such as industrial, biological, and medical investigations. It leads to the study of a ratio of binomial proportions for two populations. Previous studies have suggested that the confidence intervals of the ratio of two correlated proportions do not possess closed-form solutions. In addition,  the computation process is complex and often based on a maximum likelihood estimation which is a biased estimator of the ratio.

The talk considers the data from two dependent samples and explores the general problem of estimating the ratio of binomial proportions.  The main objective of this thesis is to propose the confidence interval for a ratio of binomial proportions for dependent populations by using the asymptotic normality method based on an application of the delta method and the nonparametric bootstrap method. Moreover, the performance of the maximum likelihood estimation is compared with other estimation methods such as method of moments estimation, Bayesian estimation, minimax estimation, and Ngamkham's estimation for an estimate of the ratio.

A simulation study in various scenarios is carried out to compare the performance of the estimators of the ratio for dependent populations. The main characteristics of the proposed confidence interval estimations will be investigated by a Monte Carlo simulation.

The result found that the proposed confidence interval possesses a closed-form solution and uncomplicated computation process. The simulation studies indicate that the proposed confidence interval estimation methods performs well based on the aforementioned criteria. Furthermore, the proposed confidence intervals are proven to be more  appropriate estimations for the ratio of binomial proportions than the existing confidence intervals.

Finally, the confidence intervals are applied with three real datasets. It shows that the proposed confidence interval can be effectively applied in several subject areas.

Keywords: Ration of binomial proportions, Dependent samples, Direct binomial sampling scheme, Inverse binomial sampling scheme, Asymptotic confidence limits, Logarithmic confidence interval, Monte Carlo simulation.