Electronic Journal of Statistics

Adaptive density estimation in the pile-up model involving measurement errors

Fabienne Comte and Tabea Rebafka

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Abstract

Motivated by fluorescence lifetime measurements, this paper considers the problem of nonparametric density estimation in the pile-up model, where observations suffer also from measurement errors. In the pile-up model, an observation is defined as the minimum of a random number of i.i.d. variables following the target distribution. Adaptive nonparametric estimators are proposed for this pile-up model with measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation method is assessed by a simulation study and the application to real fluorescence lifetime data.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 2002-2037.

Dates
First available in Project Euclid: 2 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1351865116

Digital Object Identifier
doi:10.1214/12-EJS737

Mathematical Reviews number (MathSciNet)
MR3020255

Zentralblatt MATH identifier
1295.62037

Subjects
Primary: 62G07: Density estimation 62N01: Censored data models

Keywords
Adaptive nonparametric estimation biased data deconvolution fluorescence lifetimes projection estimator

Citation

Comte, Fabienne; Rebafka, Tabea. Adaptive density estimation in the pile-up model involving measurement errors. Electron. J. Statist. 6 (2012), 2002--2037. doi:10.1214/12-EJS737. https://projecteuclid.org/euclid.ejs/1351865116


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