[hal-00727526] Nonparametric regression on hidden phi-mixing variables identifiability and consistency of a pseudo-likelihood based estimation procedure

This paper outlines a new nonparametric estimation procedure for unobserved phi-mixing processes It is assumed that the only information on the stationary hidden states Xk is given by the process Yk where Yk is a noisy observation of fXk The paper introduces a maximum pseudo-likelihood procedure to estimate the function f and the distribution of the hidden states using blocks of observations of length b The identifiability of the model is studied in the particular cases b=1 and b=2 The consistency of the estimators of f and of the distribution of the hidden states as the number of observations grows to infinity is established



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