Electronic Journal of Statistics

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

Alexander Meister, Ulrich Stadtmüller, and Christian Wagner

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 36-57.

Dates
First available in Project Euclid: 19 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1263911324

Digital Object Identifier
doi:10.1214/09-EJS444

Mathematical Reviews number (MathSciNet)
MR2645477

Zentralblatt MATH identifier
1329.62189

Subjects
Primary: 62G07: Density estimation

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

Citation

Meister, Alexander; Stadtmüller, Ulrich; Wagner, Christian. Density deconvolution in a two-level heteroscedastic model with unknown error density. Electron. J. Statist. 4 (2010), 36--57. doi:10.1214/09-EJS444. https://projecteuclid.org/euclid.ejs/1263911324


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