This article is cited in 9 papers

Nonparametric estimation of smooth spectral densities of Gaussian stationary sequences

G. K. Golubev

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: 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.

Keywords: stationary Gaussian sequence, spectral density, linear estimate, mean square risk, family of neighborhoods, asymptotically minimax estimate.

Received: 16.10.1990

 English version: Theory of Probability and its Applications, 1993, 38:4, 630–639

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