A note on simulataneous confidence intervals for multinomial proportions

Abstract

Construction of simultaneous confidence intervals for multinomial proportions plays a crucial role in many areas of applied statistics. Recently, Sison and Glaz (1995, Journal of the American Statistical Association, 90, 366–369) recommended two approaches for constructing the two-sided confidence intervals. However, the performance of the first approach is basically dependent on the configurations of unknown population proportions, and the second approach needs enormous computational time In this paper we introduce a new approach for evaluating the multinomial distribution and then propose a procedure for constructing two different forms of one-sided simultaneous confidence intervals for multinomial proportions. The simulation study reveals that the performance of the new procedure is very robust to any configurations of population proportions provided that the sample size is sufficiently large. Besides, the computational time of applying the procedure is trivial.

Keywords:

• Multivariate Normal Distribution
• Negative Product Correlation
• One-Sided
• Poisson Distribution