This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient.
"Semi-parametric second-order efficient estimation of the period of a signal." Bernoulli 13 (4) 910 - 932, November 2007. https://doi.org/10.3150/07-BEJ5077