Abstract:
The author considers the nonparametric problem of estimating the unknown spectral density of a stationary Gaussian sequence on the basis of observations of it in additive Gaussian noise. A lower bound for the minimax risk, asymptotic with respect to the number of observations, is established. It is shown that for an extensive class of spectral densities, including rational spectral densities, this bound is attained on linear estimation plan. In the general case, linear estimation plans are asymptotically efficient with respect to the order of the number of observations.
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