Efficient estimation for a subclass of shape invariant models

Details Efficient estimation for a subclass of shape invariant models Efficient estimation for a subclass of shape invariant models

2010-10-05

arxiv.org/abs/1010.0796v1

Annals of Statistics 2010, Vol. 38, No. 3, 1885-1912

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS566 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS566

In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common shape is unknown, we introduce an asymptotically efficient estimator of the finite-dimensional parameter (phases and amplitude) using the profile likelihood and the Fourier basis. Moreover, this estimation method leads to a consistent and asymptotically linear estimator for the common shape.

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