Simultaneous Confidence Intervals and Sample Size Determination for Multinomial Proportions

TLDR

Simultaneous confidence interval procedures for multinomial proportions are widely used in many scientific fields. The article introduces two new simultaneous confidence interval procedures for multinomial proportions. The authors evaluate the procedures via numerical simulations, comparing their performance to established methods. The new procedures outperform established ones in accuracy and sample‑size savings, and, since they perform equally well, the faster one is recommended.

Abstract

Abstract Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature. From the results presented in this article, it is evident that the new procedures are more accurate than the established ones, where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves. In the sample size determination problem, the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications. Because both procedures performed equally well, the procedure that requires the least amount of computing time is recommended.