Semi-parametric second-order efficient estimation of the period of a signal

Details Semi-parametric second-order efficient estimation of the period of a signal Semi-parametric second-order efficient estimation of the period of a signal

2007-11-26

arxiv.org/abs/0711.3955v1

Bernoulli 2007, Vol. 13, No. 4, 910-932

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ5077 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ5077

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.

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