Estimation of Square-Integrable Density on the Basis of a Sequence of Observations

We consider nonparametric estimation of the spectral density. It is assumed that the correlation coefficients satisfy the inequality $\sum^{\infty}_{j=-\infty}a_j\theta^2_j\leq Q$, $a_j\geq 0$, $Q>0$. Asymptotically exact estimates for the minimax mean-square risk are obtained. A consistent and asymptotically efficient linear estimation plan is constructed.