Nonparametric Estimation for some Specific Classes of Hidden Markov Models.

Stéphan Clémençon (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the problem of nonparametric estimation of the stationary and transition densities of a regular Markov chain based on noisy observations when the density of the noise's terms k(x) has a Fourier transform with decay of order |w|−α as w → ∞. Adopting the formalism of the wavelet-vaguelette decomposition (WVD), we propose estimation procedures based on thresholding of the WVD coefficients which are shown to be nearly optimal over a wide range of Besov classes for the variety of global Lp0 error measures, 1 6 p0 < ∞.

Mots clés: Wavelet-vaguelette decomposition; noisy Markov models; deconvolution

Domaines: Statistiques [math.ST]

Stéphan Clémençon. Nonparametric Estimation for some Specific Classes of Hidden Markov Models.. 2007. ⟨hal-00141921⟩