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On the estimation of frequency in point-process data

Published online by Cambridge University Press:  14 July 2016

D. Vere-Jones
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Abstract

Suppose that it is desired to determine the frequency, known to lie in a range 0 < σ ≦ ω ≦ ΩT <∞, of a periodic effect modulating the rate of occurrence of a Poisson point process. It is shown that if ΩT increases sufficiently slowly with T, the length of the observation period, then the frequency corresponding to the maximum of the Bartlett periodogram over this range provides a consistent estimate of the unknown frequency. The asymptotic covariance matrix is found for the maximum likelihood estimates of the parameters in a cyclic Poisson model, and the close analogue with frequency estimation for Gaussian processes is emphasized. It is pointed out, however, that in the point-process case periodogram estimates will be efficient only for very special models.

Keywords

POINT PROCESSFREQUENCY ESTIMATIONPERIODOGRAMASYMPTOTIC COVARIANCE MATRIXMAXIMUM LIKELIHOOD ESTIMATESPOISSON PROCESSGAUSSIAN PROCESSCONSISTENCYLIKELIHOOD ANALYSIS
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 383 - 394
Copyright
Copyright © 1982 Applied Probability Trust 

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References

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