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Random thresholds for linear model selection

Published online by Cambridge University Press:  23 January 2008

Marc Lavielle  and
Carenne Ludeña
Marc Lavielle
Affiliation:
University Paris-Sud and University René Descartes, France; Marc.Lavielle@math.u-psud.fr
Carenne Ludeña
Affiliation:
IVIC, Venezuela; cludena@ivic.ve
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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.

Keywords

Adaptive estimationlinear model selectionhard thresholdingrandom thresholdingL-statistics
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 173 - 195
Copyright
© EDP Sciences, SMAI, 2008

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