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June, 1962 Spectral Analysis with Regularly Missed Observations
Richard H. Jones
Ann. Math. Statist. 33(2): 455-461 (June, 1962). DOI: 10.1214/aoms/1177704572


Estimating the spectral density of a discrete stationary stochastic process is studied for the case when the observations consist of repeated groups of $\alpha$ equally spaced observations followed by $\beta$ missed observations, $(\alpha > \beta)$. The asymptotic variance of the estimate is derived for normally distributed variables. It is found that this variance depends not only on the value of the spectral density being estimated, but also on the spectral density at the harmonic frequencies brought in by the periodic method of sampling. Curves are presented for $\beta = 1$ showing the increase in the standard deviation and effective decrease in sample size as a function of $\alpha$.


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Richard H. Jones. "Spectral Analysis with Regularly Missed Observations." Ann. Math. Statist. 33 (2) 455 - 461, June, 1962.


Published: June, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0114.34503
MathSciNet: MR139250
Digital Object Identifier: 10.1214/aoms/1177704572

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 2 • June, 1962
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