Identifiability and consistency results for nonparametric regression models with latent data

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Seminar Probabilités & Statistique

7/04/2016 - 14:00 Sylvain Le Corff (Département de Mathématiques de l'Université Paris Sud / CNRS) Salle 2 - Tour IRMA

This talk will focus on nonparametric regression models with latent data (with unobserved regressors). The hidden states are only observed through a nonparametric curve f characterizing the pattern which has to be estimated. We will first present identifiability results in a general setting along with consistency of a pseudo likelihood based estimation procedure. Then, a new
model for time series with a specific oscillation pattern is proposed. The identifiability of the model is established under mild assumptions on the
pattern. Then, a new method for statistical inference based on Sequential Monte Carlo methods (in this case a particle smoother) and a nonparametric Expectation Maximization algorithm is developed. The potential of the method for practical applications is demonstrated through simulations and an application to human electrocardiogram recordings.