ABSTRACT
This chapter describes the statistical inference of nonparametric finite mixtures. It reviews situations where identifiability has been proved, and where inference thus can be meaningful. The chapter discusses some related questions and extensions to other nonparametric mixture models. It considers mixtures of two populations under specific restrictions on the emission densities and analyses the mixtures of translated densities. The chapter focuses on the link between hidden Markov model and multidimensional mixtures appears and deals with multivariate mixtures. The chapter argues that when the observations are at least three-dimensional and the coordinates are conditionally independent, the emission distributions are the tensor products of the marginal distributions of the coordinates, then identifiability holds under a simple linear independence assumption. It presents nonparametric inference based on spectral methods. Computing the efficient Fisher information throws light on the loss occurring due to the fact that the nonparametric emission distributions are unknown.
