  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 f(Xk). 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.
