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

Lin Yang

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 3, 744-766

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→+∞. 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.

Date: 2022
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DOI: 10.1080/03610926.2020.1754856

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