Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 2 (2017), 3141-3164.
Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family
We address the question of estimating Kullback-Leibler losses rather than squared losses in recovery problems where the noise is distributed within the exponential family. Inspired by Stein unbiased risk estimator (SURE), we exhibit conditions under which these losses can be unbiasedly estimated or estimated with a controlled bias. Simulations on parameter selection problems in applications to image denoising and variable selection with Gamma and Poisson noises illustrate the interest of Kullback-Leibler losses and the proposed estimators.
Electron. J. Statist. Volume 11, Number 2 (2017), 3141-3164.
Received: May 2016
First available in Project Euclid: 29 August 2017
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Deledalle, Charles-Alban. Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family. Electron. J. Statist. 11 (2017), no. 2, 3141--3164. doi:10.1214/17-EJS1321. https://projecteuclid.org/euclid.ejs/1503972028.