# An adaptable generalization of Hotelling's T2 test in high dimension

arXiv: https://arxiv.org/abs/1609.08725 · HTML: https://mlsanity.com/paper/1609.08725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [Adaptive Uncertainty Estimation via High-Dimensional Testing on Latent Representations](https://mlsanity.com/paper/2310.16587/) (2023)

## Abstract (arXiv)

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's T2. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the ridge-regularized Hotelling's T2 is established and used to derive the cut-off values of the proposed test. Large sample properties are verified for a class of sub-Gaussian distributions. Through an extensive simulation study, the composite test is shown to compare favorably against a host of existing two-sample test procedure in a wide range of settings. The performance of the proposed test procedure is illustrated through an application to a breast cancer data set where the goal is to detect the pathways with different DNA copy number alterations across breast cancer subtypes.