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Issue ESAIM: PS
Volume 12
Page(s) 173 - 195
DOI 10.1051/ps:2007047
Published online 23 January 2008

ESAIM: PS, 2008, Vol. 12, p. 173-195
DOI: 10.1051/ps:2007047

Random thresholds for linear model selection

Marc Lavielle1 and Carenne Ludeña2

1  University Paris-Sud and University René Descartes, France; Marc.Lavielle@math.u-psud.fr
2  IVIC, Venezuela; cludena@ivic.ve


Received October 9, 2006. Published online 23 January 2008

Abstract
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.


Mathematics Subject Classification. 62F12, 62G05, 62P99

Key words: Adaptive estimation, linear model selection, hard thresholding, random thresholding, L-statistics


© EDP Sciences, SMAI 2008


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