The Annals of Statistics

Efficient estimation for a subclass of shape invariant models

Myriam Vimond

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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.

Article information

Ann. Statist., Volume 38, Number 3 (2010), 1885-1912.

First available in Project Euclid: 14 April 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J02: General nonlinear regression 62F12: Asymptotic properties of estimators
Secondary: 62G05: Estimation

Shape invariant model semiparametric estimation efficiency discrete Fourier transform


Vimond, Myriam. Efficient estimation for a subclass of shape invariant models. Ann. Statist. 38 (2010), no. 3, 1885--1912. doi:10.1214/07-AOS566.

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