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Biometrika 1976 63(3):507-512; doi:10.1093/biomet/63.3.507
© 1976 by Biometrika Trust
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Frequency estimation from crossings of an observed mean level

ÅKE BJÖRNHAM and LINDGREN GEORG

Institute of Mathematics and Statistics, University of Umeå Sweden

By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. If the mean level is unknown and estimated from the observed mean level, then this crossing estimator is more or less biased, depending on the length of the observation interval. It is shown that if the interval is at least two mean wavelengths, then the bias is small and of the same order as the standard deviation of a certain unbiased zero crossing estimator. Therefore the crossing method gives a simple and reliable technique for automatic estimation of the mean frequenoy of a process over long periods of time, which may involve changes in the mean level and covariance function.

Key Words: Estimation of the mean • Level crossings • Mean frequency • Spectral moment • Stationary normal process • Time series estimation


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