The Annals of Statistics

Efficient estimation for a subclass of shape invariant models

Myriam Vimond

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Abstract

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

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

Dates
First available in Project Euclid: 14 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1271271281

Digital Object Identifier
doi:10.1214/07-AOS566

Mathematical Reviews number (MathSciNet)
MR2662362

Zentralblatt MATH identifier
1189.62057

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

Keywords
Shape invariant model semiparametric estimation efficiency discrete Fourier transform

Citation

Vimond, Myriam. Efficient estimation for a subclass of shape invariant models. Ann. Statist. 38 (2010), no. 3, 1885--1912. doi:10.1214/07-AOS566. https://projecteuclid.org/euclid.aos/1271271281


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