Random thresholds for linear model selection
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 173-195.

A method is introduced to select the significant or non null mean terms among a collection of independent random variables. As an application we consider the problem of recovering the significant coefficients in non ordered model selection. The method is based on a convenient random centering of the partial sums of the ordered observations. Based on $L$-statistics methods we show consistency of the proposed estimator. An extension to unknown parametric distributions is considered. Simulated examples are included to show the accuracy of the estimator. An example of signal denoising with wavelet thresholding is also discussed.

DOI : https://doi.org/10.1051/ps:2007047
Classification : 62F12,  62G05,  62P99
Mots clés : adaptive estimation, linear model selection, hard thresholding, random thresholding, $L$-statistics
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author = {Lavielle, Marc and Lude\~na, Carenne},
title = {Random thresholds for linear model selection},
journal = {ESAIM: Probability and Statistics},
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publisher = {EDP-Sciences},
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year = {2008},
doi = {10.1051/ps:2007047},
mrnumber = {2374637},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2007047/}
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Lavielle, Marc; Ludeña, Carenne. Random thresholds for linear model selection. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 173-195. doi : 10.1051/ps:2007047. http://www.numdam.org/articles/10.1051/ps:2007047/

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