Spatial-Sign based High-Dimensional Location Test

TL;DR

This paper introduces a robust, scalar-invariant test for high-dimensional mean vector testing based on spatial signs, demonstrating asymptotic normality and strong performance across various distributions.

Contribution

The paper presents a novel spatial-sign based test for high-dimensional mean vectors that is robust, scalar-invariant, and asymptotically normal under elliptical distributions.

Findings

Test is robust and efficient across diverse distributions

Asymptotic normality established for the proposed test

Simulation results confirm superior performance

Abstract

In this paper, we consider the problem of testing the mean vector in the high dimensional settings. We proposed a new robust scalar transform invariant test based on spatial sign. The proposed test statistic is asymptotically normal under elliptical distributions. Simulation studies show that our test is very robust and efficient in a wide range of distributions.