Semiparametric second order efficient estimation of the period of a signal and applications
Ismael Castillo
Bernoulli 2005.

Abstract

We consider the problem of estimating the period of an unknown periodic function in Gaussian white noise. We construct a class of estimators of the period by a penalized maximum likelihood method. We obtain a second order asymptotic expansion of the risk of such estimators and construct a second order efficient estimator when the unknown function belongs to some known class.

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