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Generalized and smooth James-Stein model selection

ContributorsSardy, Sylvain
Publication date2010
Abstract

The generalized and smooth James-Stein thresholding functions link and extend the thresholding functions employed by the James-Stein estimator, the block- and adaptive-lasso in variable selection, and the soft-, hard- and block-thresholding in wavelet smoothing. The estimator is indexed by two hyperparameters for more flexibility and a smoothness parameter for better estimation of its ℓ2-risk with the Stein unbiased risk estimate (SURE). For blocks of a fixed size, a situation that arises when observing concomitant signals (e.g., gravitational wave bursts), we derive a universal threshold, an information criterion and an oracle inequality for block thresholding. Smooth James-Stein thresholding can also be employed in parametric regression for variable selection. In that case a unique smooth estimate is defined, its smooth SURE is derived, which provides the equivalent degrees of freedom of adaptive lasso as a side result. The new estimator enjoys smoothness like ridge regression and performs variable selection like lasso.

Citation (ISO format)
SARDY, Sylvain. Generalized and smooth James-Stein model selection. 2010.
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accessLevelPublic
Identifiers
  • PID : unige:12040
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Technical informations

Creation09/23/2010 2:31:00 PM
First validation09/23/2010 2:31:00 PM
Update time03/14/2023 4:07:15 PM
Status update03/14/2023 4:07:15 PM
Last indexation01/15/2024 9:41:20 PM
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