Open Access
2011 Semiparametric shift estimation based on the cumulated periodogram for non-regular functions
Ismaël Castillo, Eric Cator
Electron. J. Statist. 5: 102-126 (2011). DOI: 10.1214/11-EJS599


The problem of estimating the center of symmetry of a symmetric signal in Gaussian white noise is considered. The underlying nuisance function f is not assumed to be differentiable, which makes a new point of view to the problem necessary.

We investigate the well-known sieve maximum likelihood estimators based on the cumulated periodogram, and study minimax rates over classes of irregular functions. It is shown that if the class appropriately controls the growth to infinity of the Fisher information over the sieve, semiparametric fast rates of convergence are obtained. We prove a lower bound result which implies that these semiparametric rates are really slower than the parametric ones, contrary to the regular case. Our results also suggest that there may be room to improve on the popular cumulated periodogram estimator.


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Ismaël Castillo. Eric Cator. "Semiparametric shift estimation based on the cumulated periodogram for non-regular functions." Electron. J. Statist. 5 102 - 126, 2011.


Published: 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1274.62230
MathSciNet: MR2773610
Digital Object Identifier: 10.1214/11-EJS599

Primary: 62G05 , 62G20

Keywords: estimation of the center of symmetry , Gaussian white noise models , non-regular case , semi-parametric models

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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