Semiparametric two-sample mixture components comparison test

We consider in this paper 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 Chi-squared type testing procedure able to compare pairwise the unknown components, i.e. to test the equality of their residual features densities. An intensive 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 two real cases: i) mortality datasets, where results show that the test remains robust even in challenging situations where the unknown component only represents a small percentage of the global population, ii) galaxy velocities datasets, where stars luminosity mixed with the Milky Way are compared.