ABSTRACT
The topic of this chapter is statistical inference of nonparametric finite mixtures. The latent variables (and thus the observations) will be mostly taken to be independent and identically distributed (i.i.d.), but in some cases they will be possibly non-independently distributed. For each observation, the corresponding latent variable indicates from which population the observation comes. In particular, when the latent variables form a Markov chain, the observation process will come from a nonparametric hidden Markov model (HMM) with finite state space. We would like to emphasize the fact that nonparametric modelling will only cover the conditional distribution of the observations given the latent variables, excluding the mixing distribution. Nonparametric modelling of the mixing distribution (with possibly infinitely denumerable or continuous support) is considered in Chapter 6.
