Nonparametric regression on hidden phi-mixing variables: identifiability and consistency of a pseudo-likelihood based estimation procedure

Thierry Dumont (1, 2) , Sylvain Le Corff (3)

1 MODAL'X - Modélisation aléatoire de Paris X
2 FP2M - Fédération Parisienne de Modélisation Mathématique
3 Département de Mathématiques-Université de Paris XI

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.

Mots clés: Identifiability; Nonparametric Estimation; Hidden variables; Maximum Likelihood

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Thierry Dumont, Sylvain Le Corff. Nonparametric regression on hidden phi-mixing variables: identifiability and consistency of a pseudo-likelihood based estimation procedure. Bernoulli, 2017, 23 (2), pp.990-1021. ⟨10.3150/15-BEJ767⟩. ⟨hal-00727526v5⟩