Robust Estimation in Finite Mixture Models

We observe a n -sample, the distribution of which is assumed to belong, or at least be close enough, given mixture model. propose an estimator this that belongs our model and possesses some robustness properties with respect possible misspecification it. establish non-asymptotic deviation bound for Hellinger distance between target its when consists densities belong VC-subgraph classes. Under suitable assumptions well-specified, we derive risk bounds parameters mixture. Finally, design statistical procedure allows us select from data number components as well models each are involved in These chosen among collection candidate ones show selection rule combined estimation strategy result satisfies oracle-type inequality.