Open Access
May 2008 Density estimation with heteroscedastic error
Aurore Delaigle, Alexander Meister
Bernoulli 14(2): 562-579 (May 2008). DOI: 10.3150/08-BEJ121

Abstract

It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for homoscedastic errors become inconsistent. In this paper, we introduce a kernel estimator of a density in the case of heteroscedastic contamination. We establish consistency of the estimator and show that it achieves optimal rates of convergence under quite general conditions. We study the limits of application of the procedure in some extreme situations, where we show that, in some cases, our estimator is consistent, even when the scaling parameter of the error is unbounded. We suggest a modified estimator for the problem where the distribution of the errors is unknown, but replicated observations are available. Finally, an adaptive procedure for selecting the smoothing parameter is proposed and its finite-sample properties are investigated on simulated examples.

Citation

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Aurore Delaigle. Alexander Meister. "Density estimation with heteroscedastic error." Bernoulli 14 (2) 562 - 579, May 2008. https://doi.org/10.3150/08-BEJ121

Information

Published: May 2008
First available in Project Euclid: 22 April 2008

zbMATH: 1155.62023
MathSciNet: MR2544102
Digital Object Identifier: 10.3150/08-BEJ121

Keywords: bandwidth , density deconvolution , errors-in-variables , heteroscedastic contamination , Inverse problems , plug-in

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

Vol.14 • No. 2 • May 2008
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