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

TL;DR

This paper proposes a new nonparametric estimation method for hidden phi-mixing processes, demonstrating identifiability and consistency of the pseudo-likelihood estimators for the hidden states and functions.

Contribution

It introduces a maximum pseudo-likelihood approach for estimating hidden functions and distributions in phi-mixing processes, with proven identifiability and consistency.

Findings

Identifiability established for block sizes b=1 and b=2.

Consistency of estimators proven as sample size increases.

Method effectively estimates hidden states and functions in noisy observations.

Abstract

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.