Order thresholding

TL;DR

Order thresholding is a flexible new statistical method based on L-statistics that enhances power in high-dimensional testing scenarios and extends to high-dimensional ANOVA, outperforming traditional thresholding techniques.

Contribution

Introduces a novel order thresholding method based on L-statistics, offering improved power and flexibility over existing thresholding approaches, applicable beyond normal distributions.

Findings

Outperforms soft and hard thresholding in simulations

Flexible threshold parameter choice enhances adaptability

Effective extension to high-dimensional ANOVA

Abstract

A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of the threshold parameter. This results in improved power over the soft and hard thresholding methods. Moreover, order thresholding is not restricted to the normal distribution. An extension of the basic order threshold statistic to high-dimensional ANOVA is presented. The performance of the basic order threshold statistic and its extension is evaluated with extensive simulations.