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June 2010 Efficient estimation for a subclass of shape invariant models
Myriam Vimond
Ann. Statist. 38(3): 1885-1912 (June 2010). DOI: 10.1214/07-AOS566


In this paper, we observe a fixed number of unknown 2π-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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Myriam Vimond. "Efficient estimation for a subclass of shape invariant models." Ann. Statist. 38 (3) 1885 - 1912, June 2010.


Published: June 2010
First available in Project Euclid: 14 April 2010

zbMATH: 1189.62057
MathSciNet: MR2662362
Digital Object Identifier: 10.1214/07-AOS566

Primary: 62F12 , 62J02
Secondary: 62G05

Keywords: discrete Fourier transform , efficiency , Semiparametric estimation , Shape invariant model

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
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