Skip to Main content Skip to Navigation
Journal articles

The two-sample problem for Poisson processes: adaptive tests with a non-asymptotic wild bootstrap approach

Abstract : Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The corresponding critical values are constructed from a non-asymptotic wild bootstrap approach, leading to level \alpha tests. Various choices for the kernel functions are possible, including projection, approximation or reproducing kernels. In this last case, we obtain a parametric rate of testing for a weak metric defined in the RKHS associated with the considered reproducing kernel. Then we introduce, in the other cases, an aggregation procedure, which allows us to import ideas coming from model selection, thresholding and/or approximation kernels adaptive estimation. The resulting multiple tests are proved to be of level \alpha, and to satisfy non-asymptotic oracle type conditions for the classical L2-norm. From these conditions, we deduce that they are adaptive in the minimax sense over a large variety of classes of alternatives based on classical and weak Besov bodies in the univariate case, but also Sobolev and anisotropic Nikol'skii-Besov balls in the multivariate case.
Complete list of metadatas

Cited literature [50 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00679102
Contributor : Patricia Reynaud-Bouret <>
Submitted on : Tuesday, November 13, 2012 - 2:02:44 PM
Last modification on : Thursday, January 7, 2021 - 4:33:19 PM
Long-term archiving on: : Thursday, February 14, 2013 - 3:42:20 AM

Files

RevisionTestEga.pdf
Files produced by the author(s)

Identifiers

Citation

Magalie Fromont, Béatrice Laurent, Patricia Reynaud-Bouret. The two-sample problem for Poisson processes: adaptive tests with a non-asymptotic wild bootstrap approach. Annals of Statistics, Institute of Mathematical Statistics, 2013, 41 (3), pp.1431-1461. ⟨10.1214/13-AOS1114⟩. ⟨hal-00679102v2⟩

Share

Metrics

Record views

1541

Files downloads

690