Parameter recovery in two-component contamination mixtures: the ${\mathbb{L}}^2$ strategy

Abstract

In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, $f^{\star }=(1-{\lambda }^{\star })\varphi +{\lambda }^{\star }\varphi (.-{\mu }^{\star })$, where the shape $\varphi$ is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters $({\lambda }^{\star },{\mu }^{\star })$. In particular, we prove that the classical parametric rate $1/\sqrt{n}$ cannot be reached when at least one of these parameters is allowed to tend to $0$ with $n$.

48 pages, 4 figures

References in corpus (1)

• Inference for mixtures of symmetric distributions