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 $(X_{k})_{k\ge0}$ is given by the process $(Y_{k})_{k\ge0}$, where $Y_{k}$ is a noisy observation of $f_{\star}(X_{k})$. The paper introduces a maximum pseudo-likelihood procedure to estimate the function $f_{\star}$ and the distribution $\nu_{b,\star}$ of $(X_{0},\ldots,X_{b-1})$ using blocks of observations of length $b$. The identifiability of the model is studied in the particular cases $b=1$ and $b=2$ and the consistency of the estimators of $f_{\star}$ and of $\nu_{b,\star}$ as the number of observations grows to infinity is established.
Citation
Thierry Dumont. Sylvain Le Corff. "Nonparametric regression on hidden $\Phi$-mixing variables: Identifiability and consistency of a pseudo-likelihood based estimation procedure." Bernoulli 23 (2) 990 - 1021, May 2017. https://doi.org/10.3150/15-BEJ767
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