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The estimation of frequency

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
The Australian National University
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Abstract

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ0, is in fact 0 or <it is shown that the estimate, , satisfies for N ≧ N0 (ω) where N0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.

Keywords

FREQUENCYREGRESSION ON HARMONICSNON-LINEAR REGRESSIONSTRONG LAWCENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 510 - 519
Copyright
Copyright © Applied Probability Trust 1973 

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