Asymptotically optimal spectral estimation with applications to small samples
Philip J. Ramsey, Robert V. Foutz · Communications in Statistics - Simulation and Computation · 1996
A general technique is described for estimating spectral parameters for multiple time series, including spectral densities, coherence, phase, and group delay. When an “ideal” condition is met the technique gives uniformly minimum variance unbiased estimators and confidence intervals that have confidence coefficients no smaller than a prespecified value. The technique is called asymptotically optimal, since the ideal condition is met asymptotically as sample sizes increase under general conditions. The standard procedures for spectral estimation are asymptotic and are intended for use in large samples. This article proposes yet another asymptotic procedure primarily because the ideal condition for its optimality is known to hold to a good degree of approximation when sample sizes are not too small. For this reason the procedure is meant to be of practical use for moderate sample sizes. The procedure is also meant to be of use for small sample sizes after the data have been transformed to improve the degree to which the ideal condition approximately holds.