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June, 1971 The Exact Error in Spectrum Estimates
Henry R. Neave
Ann. Math. Statist. 42(3): 961-975 (June, 1971). DOI: 10.1214/aoms/1177693325


Since the asymptotic expression for the variance of estimators of the spectrum of a stationary time series was derived, it has often been used as an approximation to the variance of estimators using finite samples. Little attempt seems to have been made to investigate the nature of the convergence to the asymptotic form. In this paper an exact expression for the variance is derived on the additional assumption that the time series is a normal process, and is used to study estimators of various different spectra. A philosophy for choosing spectrum estimators is proposed which attempts to place the two forms of error, bias and variance, in their true perspective.


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Henry R. Neave. "The Exact Error in Spectrum Estimates." Ann. Math. Statist. 42 (3) 961 - 975, June, 1971.


Published: June, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0225.62113
Digital Object Identifier: 10.1214/aoms/1177693325

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 3 • June, 1971
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