Continuous testing for Poisson process intensities: A new perspective on scanning statistics
Methodology
2017-05-25 v1
Abstract
We propose a novel continuous testing framework to test the intensities of Poisson Processes. This framework allows a rigorous definition of the complete testing procedure, from an infinite number of hypothesis to joint error rates. Our work extends traditional procedures based on scanning windows, by controlling the family-wise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. The decision rule is based on a \pvalue process that can be estimated by a Monte-Carlo procedure. We also propose new test statistics based on kernels. Our method is applied in Neurosciences and Genomics through the standard test of homogeneity, and the two-sample test.
Cite
@article{arxiv.1705.08800,
title = {Continuous testing for Poisson process intensities: A new perspective on scanning statistics},
author = {Franck Picard and Patricia Reynaud-Bouret and Etienne Roquain},
journal= {arXiv preprint arXiv:1705.08800},
year = {2017}
}