Open Access
2010 Density deconvolution in a two-level heteroscedastic model with unknown error density
Alexander Meister, Ulrich Stadtmüller, Christian Wagner
Electron. J. Statist. 4: 36-57 (2010). DOI: 10.1214/09-EJS444


We consider a statistical experiment where two types of contaminated data are observed. Therein, both data sets are affected by additive measurement errors but the scaling factors of the error density may be different and/or the observations have been averaged over different numbers of independent replicates. That kind of heteroscedasticity of the data allows us to identify the target density although the error density is unknown and we can allow that the characteristic function of the error variables may have zeros. We introduce a novel nonparametric procedure which estimates the target density with nearly optimal convergence rates. The main goal in this paper is to derive the upper and lower bounds for the convergence rates. A small simulation study addresses the finite sample properties of the procedure.


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Alexander Meister. Ulrich Stadtmüller. Christian Wagner. "Density deconvolution in a two-level heteroscedastic model with unknown error density." Electron. J. Statist. 4 36 - 57, 2010.


Published: 2010
First available in Project Euclid: 19 January 2010

zbMATH: 1329.62189
MathSciNet: MR2645477
Digital Object Identifier: 10.1214/09-EJS444

Primary: 62G07

Keywords: Hermite polynomials , Measurement errors , Minimax convergence rates , nonparametric statistics , Statistical inverse problems

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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