Multiple Comparison Procedures for Poisson Parameters in Multi-Sample Models

Abstract

First, we consider multiple comparisons for the differences among parameters in k Poisson populations. We may give the Tukey-Kramer type multiple test procedure based on estimators of k means. However, the degree of conservativeness for the multiple tests depends on unknown rate parameters. Therefore, multiple tests based on estimators of k standard deviations are proposed. It is found that the degree of con-servativeness for the proposed tests is controlled by the sample sizes. Furthermore, the closed testing procedure, more powerful than the REGW (Ryan/Einot-Gabriel/Welsch) tests, is proposed. Simultaneous confidence intervals for the differences of the square roots of the rates are discussed. Next, for the multiple comparisons with a control, we propose the multiple test procedure based on the estimators of k standard deviations. It is shown that the proposed multiple test is superior to the tests based on the Bonferroni inequality asymptotically. A sequentially rejective procedure is derived under unequal sample sizes.