Note on High Dimensional Spatial-Sign Test for One Sample Problem

Ping Zhao; Long Feng

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arXiv · 2601.08736

Note on High Dimensional Spatial-Sign Test for One Sample Problem

Ping Zhao·Long Feng

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Abstract

We revisit the null distribution of the high-dimensional spatial-sign test of Wang et al. (2015) under mild structural assumptions on the scatter matrix. We show that the standardized test statistic converges to a non-Gaussian limit, characterized as a mixture of a normal component and a weighted chi-square component. To facilitate practical implementation, we propose a wild bootstrap procedure for computing critical values and establish its asymptotic validity. Numerical experiments demonstrate that the proposed bootstrap test delivers accurate size control across a wide range of dependence settings and dimension-sample-size regimes.

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Ping Zhao, Long Feng. 2026-01-13. Note on High Dimensional Spatial-Sign Test for One Sample Problem. https://arxiv.org/abs/2601.08736

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