Inverse Norm Weighted Maxsum Test for High Dimensional Location Parameters

TL;DR

This paper introduces an inverse norm weighted maxsum test for high-dimensional location parameters, significantly improving power and robustness in sparse and heavy-tailed data scenarios.

Contribution

It proposes a novel max-type test based on weighted spatial signs and a combined max-sum procedure, enhancing detection power and robustness in high-dimensional testing.

Findings

Inverse norm test outperforms existing max-type tests in power.

The combined max-sum test is robust across various sparsity levels.

Simulation results show superior performance over traditional methods.

Abstract

In the context of high-dimensional data, we investigate the one-sample location testing problem. We introduce a max-type test based on the weighted spatial sign, which exhibits exceptional performance, particularly in the presence of sparse alternatives. Notably, we find that the inverse norm test significantly enhances the power of the test compared to several existing max-type tests. Next, we prove the asymptotic independence between the newly proposed max-type test statistic and the sum-type test statistic based on the weighted spatial sign. Then, we propose an innovative max-sum type testing procedure that integrates both test statistics. This novel procedure demonstrates remarkable robustness and effectiveness across a wide range of signal sparsity levels and heavy-tailed distributions. Through extensive simulation studies, we highlight the superior performance of the proposed method, showcasing its robustness and efficiency compared to traditional alternatives in various high-dimensional settings.