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November, 1974 On Large-Sample Estimation for the Mean of a Stationary Random Sequence
Rolf K. Adenstedt
Ann. Statist. 2(6): 1095-1107 (November, 1974). DOI: 10.1214/aos/1176342867


For a wide class of stationary random sequences possessing a spectral density function, the variance of the best linear unbiased estimator for the mean is seen to depend asymptotically only on the behavior of the spectral density near the origin. Asymptotically efficient estimators based only on this behavior may be chosen. For spectral densities behaving like $\lambda^\nu$ at the origin, $\nu > -1$ a constant, the minimum variance decreases like $n^{-\nu-1}$, where $n$ is the sample size. Asymptotically efficient estimators depending on $\nu$ are given. Finally, the consequences of over- or under-estimating the value of $\nu$ in choosing an estimator are considered.


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Rolf K. Adenstedt. "On Large-Sample Estimation for the Mean of a Stationary Random Sequence." Ann. Statist. 2 (6) 1095 - 1107, November, 1974.


Published: November, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0296.62081
MathSciNet: MR368354
Digital Object Identifier: 10.1214/aos/1176342867

Keywords: 55 , 62 , efficiency , linear estimation , ‎mean‎ , Spectral density , stationary time series

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 6 • November, 1974
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