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Density deconvolution in a two-level heteroscedastic model with unknown error density

Alexander Meister, Graduiertenkolleg 1100, Universität Ulm, Germany
Ulrich Stadtmüller, Institut für Zahlentheorie und Wahrscheinlichkeitstheorie, Universität Ulm, Germ
Christian Wagner, Institut für Zahlentheorie und Wahrscheinlichkeitstheorie, Universität Ulm, Germ


Abstract
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.

AMS 2000 subject classifications: Primary 62G07.

Keywords: Hermite polynomials, measurement errors, minimax convergence rates, nonparametric statistics, statistical inverse problems.

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Meister, Alexander, Stadtmüller, Ulrich, Wagner, Christian, Density deconvolution in a two-level heteroscedastic model with unknown error density, Electronic Journal of Statistics, , (), 36-57 (electronic). DOI: 10.1214/09-EJS444.

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Electronic Journal of Statistics. ISSN: 1935-7524