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. © 2007 ISI/BS.
|Journal||Bernoulli: A Journal of Mathematical Statistics and Probability|
|Publication status||Published - 2007|