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This paper considers hidden Markov models where the observations are given asthe sum of a latent state which lies in a general state space and someindependent noise with unknown distribution. It is shown that these fullynonparametric translation models are identifiable with respect to both thedistribution of the latent variables and the distribution of the noise, undermostly a light tail assumption on the latent variables. Two nonparametricestimation methods are proposed and we prove that the corresponding estimatorsare consistent for the weak convergence topology. These results are illustratedwith numerical experiments.

Identifiability and consistent estimation of nonparametric translation hidden Markov models with general state space