Nonparametric estimation of smooth spectral densities of Gaussian stationary sequences

he problem of spectral density estimation in the. Hilbert space norm of $L_2 (-\pi,\pi)$ is considered for a Gaussian stationary sequence. On the basis of the criterion involving the unbiased estimate for mean square risk of linear estimates we construct the class of nonlinear estimates for spectral density which are locally asymptotically minimax on the neighborhoods of smooth functions.