An Improved Test for High-Dimensional Mean Vectors and Covariance Matrices Using Random Projection

Tung-Lung Wu ()
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Tung-Lung Wu: Department of Mathematics and Statistics, Mississippi State University, 75 B.S. Hood Drive, Starkville, MS 39762, USA

Mathematics, 2025, vol. 13, issue 13, 1-24

Abstract: This paper proposes an improved random-projection-based method for testing high-dimensional two-sample mean vectors and covariance matrices, building on the framework of . By incorporating training data to guide the construction of projection matrices toward the estimated mean difference, the proposed approach substantially enhances the power of the projected Hotelling’s T 2 statistic. We introduce three aggregation strategies—maximum, average, and percentile-based—to ensure stable performance across multiple projections. Extensive simulation studies illustrate that the proposed method performs favorably compared to a recent state-of-the-art technique, particularly in detecting sparse signals, while maintaining rigorous control of the Type-I error rate.

Keywords: high-dimensional data; random projection; mean vectors; covariance matrices; hypothesis testing; large p small n (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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