Electronic Journal of Statistics

Adaptive density estimation in deconvolution problems with unknown error distribution

Johanna Kappus and Gwennaëlle Mabon

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Abstract

We investigate the data driven choice of the cutoff parameter in density deconvolution problems with unknown error distribution. To make the target density identifiable, one has to assume that some additional information on the noise is available. We consider two different models: the framework where some additional sample of the pure noise is available, as well as the model of repeated measurements, where the contaminated random variables of interest can be observed repeatedly, with independent errors. We introduce spectral cutoff estimators and present upper risk bounds. The focus of this work lies on the optimal choice of the bandwidth by penalization strategies, leading to non-asymptotic oracle bounds.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2879-2904.

Dates
First available in Project Euclid: 8 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1420726194

Digital Object Identifier
doi:10.1214/14-EJS976

Mathematical Reviews number (MathSciNet)
MR3299125

Zentralblatt MATH identifier
1308.62074

Subjects
Primary: 62G07: Density estimation
Secondary: 62G99: None of the above, but in this section

Keywords
Adaptive estimation deconvolution density estimation mean squared risk nonparametric methods replicate observations

Citation

Kappus, Johanna; Mabon, Gwennaëlle. Adaptive density estimation in deconvolution problems with unknown error distribution. Electron. J. Statist. 8 (2014), no. 2, 2879--2904. doi:10.1214/14-EJS976. https://projecteuclid.org/euclid.ejs/1420726194


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