Résumé en anglais

Rousseau et al. [8] recently studied the asymptotic behavior of Bayesian estimators in the FEXP-model for spectral densities of Gaussian time-series. For the L2-norm on the log-spectral densities, they proved that the convergence rate is at least n 2 +1 (log n) 2 +2 2 +1 , > 1 2 being the Sobolev-regularity of the true spectral density fo. We will improve upon the logarithmic factor, and prove that given a prior only depending on s > 1 2 , we have adaptivity to any s.