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Abstract:
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Hidden Markov Models are useful tools in many applied fields (genomics, facial recognition, financial time series .). In this work, we assume that the latent process is a finite state stationary Markov chain, and that the observed process is continuous and possibly multivariate. Instead of the widely used Gaussian assumption, we assume that the emission distributions admit log-concave densities. We propose a two-step estimation procedure when all emission distributions have the same shape. The first step allows to estimate the parametric part of the model, namely the number of states, the distribution of the latent process and the location parameters of the emission densities. The second step yields an estimate of the common log-concave shape of the emission densities. The procedure can be easily implemented, and does not require to calibrate any smoothing parameter in the nonparametric second step. The procedure is supported both by theoretical results based on non-asymptotic concentration inequalities and by a simulation study that also addresses the clustering performance of the method. This proves how much statistical methods are essential to recover hidden information !
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