Non-asymptotic detection of two-component mixtures with unknown means

Abstract: This work is concerned with the detection of a mixture distribution from a R-valued sample. Given a sample X1,..., Xn and an even density φ, our aim is to detect whether the sample distribution is φ(. − µ) for some unknown mean µ, or is defined as a two-component mixture based on translations of φ. In a first time, a non-asymptotic testing procedure is proposed and we determine conditions under which the power of the test can be controlled. In a second time, the performances of our testing procedure are investigated in ’benchmark ’ asymptotic settings. A simulation study provides comparisons with classical procedures.