Random threshold for linear model selection, revisited

TL;DR

This paper revisits a random thresholding method for linear model selection, proposing a modification that removes dependency on a window parameter and demonstrates improved performance in simulations and fMRI data analysis.

Contribution

It introduces a simple modification to an existing random thresholding method, enhancing its practical applicability and maintaining asymptotic properties.

Findings

The modified method removes window parameter dependency.

Simulation studies show improved binary classification risk.

Application to fMRI data demonstrates practical utility.

Abstract

In [Lavielle and Ludena 07], a random thresholding metho d is intro duced to select the significant, or non null, mean terms among a collection of independent random variables, and applied to the problem of recovering the significant coefficients in non ordered model selection. We intro duce a simple modification which removes the dep endency of the proposed estimator on a window parameter while maintaining its asymptotic properties. A simulation study suggests that both procedures compare favorably to standard thresholding approaches, such as multiple testing or model-based clustering, in terms of the binary classification risk. An application of the method to the problem of activation detection on functional magnetic resonance imaging (fMRI) data is discussed.