Multiple hypothesis testing for Poisson processes with variable change–point intensity

Abstract

Consider the multiple hypothesis problem for n independent Poisson processes whose jump size of the intensity function varies with n. The intensity function contains two types of parameters, the jump instant and the shift or scale parameter, which produces the dependence of the statistics. The Bayes multiple procedure is proposed to diminish the effect of the dependence while three other procedures are constructed in comparison. For each procedure, we describe the choice of the thresholds, the power and the general power under the local alternatives as $n\to +\infty .$ The numerical results show that the limit powers of the Bayes multiple procedure are higher than the others in the neighborhood of the null hypotheses.

KEYWORDS:

• Asymptotic behaviors
• local alternatives
• multiple test procedures
• variable change–point intensity

MSC 2010 Classification:

• 62M02
• 62H15
• 62F15

Acknowledgments

The author would like to thank the anonymous reviewers for careful reading of the manuscript and for their helpful remarks and comments.

Additional information

Funding

This work was supported by the Education and Scientific Research Project for Young and Middle-aged Teachers of Fujian Province, China (Grant number JAT190019).