A law of the iterated logarithm for an estimate of frequency

Abstract

A form of the law of the iterated logarithm is proved for the estimate of the frequency,[omega]0, of a sinusoidal oscillation when observed subject to stationary noise. The estimate,, is the location of the maximum of the periodogram from T observations. The form of the law is unusual since it is whose limit superior is a.s. finite.integrated logarithm oscillatory frequency periodogram weak mixing