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Estimation of the mean of a stationary time series by sampling

Published online by Cambridge University Press:  14 July 2016

David R. Brillinger
David R. Brillinger*
Affiliation:
University of Exeter and University of California, Berkeley
*
*Institute of Biometry and Community Medicine.
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Abstract

Let X(t), – ∞ < t < ∞, be a stationary time series with mean cx. Let 0 < τ1 < τ2 < … < τN ≦ T denote A given sampling times in the interval (0, T]. We determine the asymptotic distribution of the estimate [X(τ1) + … + X(τN)]/N of cx when the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the series X(t). The results obtained may be viewed as non-standard central limit theorems.

Keywords

STATIONARY SERIESPOINT PROCESSESCENTRAL LIMIT THEOREMSCONFIDENCE INTERVALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 419 - 431
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research partially supported by N.S.F. Grant GP-31411.

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