文章基本信息

标题：Adaptive density estimation in deconvolution problems with unknown error distribution
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作者：Johanna Kappus ; Gwennaëlle Mabon
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2014
卷号：8
期号：2
页码：2879-2904
DOI：10.1214/14-EJS976
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.