Semiparametric two-sample admixture components comparison test: The symmetric case

Abstract In this paper, we consider admixture models which are two-component mixture distributions having one known component. This is the case when a gold standard reference component is well known, and when a population contains such a component plus another one with different features. When two populations are drawn from such models, we propose a penalized χ 2 -type testing procedure allowing a pairwise comparison of the unknown components, i.e. to test the equality of their residual features densities, under a symmetry condition. A numerical study is carried out from a large range of simulation setups to illustrate the asymptotic properties of our test. Moreover the testing procedure is applied on a real-world case: galaxy velocities datasets, where stars heliocentric velocities mixed with the Milky Way are compared.