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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Two-sample contamination model test.

Pierre Vandekerkhove
LAMA, Université Gustave Eiffel
https://perso.math.u-pem.fr/vandekerkhove.pierre/

Date(s) : 31/01/2022   iCal
15h00 - 16h00

In this talk we will consider two-component mixture models having one single known component. This type of model is of particular interest when a known random phenomenon is contaminated by an unknown random effect.

We propose in this setup to test the equality in distribution of the unknown random sources involved in two separate samples generated from such a model. For this purpose, we introduce the so-called IBM (Inversion-Best Matching) approach resulting in a tuning-free relaxed semiparametric Cramér-von Mises type two-sample test requiring minimal assumptions about the unknown distributions. The accomplishment of our work lies in the fact

that we establish, under some natural and interpretable mutual-identifiability conditions specific to the two-sample case, a functional central limit theorem about the proportion parameters along with the unknown cumulative distribution functions of the model. An intensive numerical study is carried out from a large range of simulation setups to illustrate the asymptotic properties of our test. Finally, our testing procedure, implemented in the admix

R package, is applied to a real-life situation through pairwise post COVID-19 mortality excess profil testing across a panel of European countries.

 

Emplacement
Saint-Charles - FRUMAM (2ème étage)

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