Open Access
August 2016 Robust estimation on a parametric model via testing
Mathieu Sart
Bernoulli 22(3): 1617-1670 (August 2016). DOI: 10.3150/15-BEJ706


We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk bounds with respect to the Hellinger distance under mild assumptions on the parametric model. We show that the estimator is robust even for models for which the maximum likelihood method is bound to fail. A numerical simulation illustrates its robustness properties. When the model is true and regular enough, we prove that the estimator is very close to the maximum likelihood one, at least when the number of observations $n$ is large. In particular, it inherits its efficiency. Simulations show that these two estimators are almost equal with large probability, even for small values of $n$ when the model is regular enough and contains the true density.


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Mathieu Sart. "Robust estimation on a parametric model via testing." Bernoulli 22 (3) 1617 - 1670, August 2016.


Received: 1 September 2013; Revised: 1 January 2015; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1360.62108
MathSciNet: MR3474828
Digital Object Identifier: 10.3150/15-BEJ706

Keywords: Parametric estimation , robust estimation , Robust tests , T-estimator

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 3 • August 2016
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