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.

Keywords: adaptive estimation, linear model selection, hard thresholding, random thresholding, $L$-statistics

@article{PS_2008__12__173_0, author = {Lavielle, Marc and Lude\~na, Carenne}, title = {Random thresholds for linear model selection}, journal = {ESAIM: Probability and Statistics}, pages = {173--195}, publisher = {EDP-Sciences}, volume = {12}, year = {2008}, doi = {10.1051/ps:2007047}, mrnumber = {2374637}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2007047/} }

TY - JOUR AU - Lavielle, Marc AU - Ludeña, Carenne TI - Random thresholds for linear model selection JO - ESAIM: Probability and Statistics PY - 2008 SP - 173 EP - 195 VL - 12 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007047/ DO - 10.1051/ps:2007047 LA - en ID - PS_2008__12__173_0 ER -

Lavielle, Marc; Ludeña, Carenne. Random thresholds for linear model selection. ESAIM: Probability and Statistics, Volume 12 (2008), pp. 173-195. doi : 10.1051/ps:2007047. http://www.numdam.org/articles/10.1051/ps:2007047/

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