Estimation of the density of a distribution from data with an admixture
N. Lodatko, Rostyslav Maiboroda · Theory of Probability and Mathematical Statistics · 2007
We consider the problem of estimation of a density from observations of a two-component mixture with varying concentrations. It is assumed that the distribution of the first component is unknown, while a parametric model is (perhaps) available for the second component. Applying the sieve maximum likelihood method we construct histogram-type estimators for the densities of distributions of the components and estimators for unknown parameters of the second component. We prove the consistency of the estimators and obtain estimates for the rate of convergence.