Testing the equality of multivariate means when p>n by combining the Hotelling and Simes tests

We propose a method of testing a shift between mean vectors of two multivariate Gaussian random variables in a high-dimensional setting incorporating the possible dependency and allowing p > n . This method is a combination of two well-known tests: the Hotelling test and the Simes test. The tests...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2022-06, Vol.31 (2), p.390-415
Main Authors: Frostig, Tzviel, Benjamini, Yoav
Format: Article
Language:English
Subjects:
Covariance matrix
Economics
Finance
Insurance
Management
Mathematics and Statistics
Multivariate analysis
Original Paper
Random variables
Statistical Theory and Methods
Statistics
Statistics for Business
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Summary:We propose a method of testing a shift between mean vectors of two multivariate Gaussian random variables in a high-dimensional setting incorporating the possible dependency and allowing p > n . This method is a combination of two well-known tests: the Hotelling test and the Simes test. The tests are integrated by sampling several dimensions at each iteration, testing each using the Hotelling test, and combining their results using the Simes test. We prove that this procedure is valid asymptotically. This procedure can be extended to handle non-equal covariance matrices by plugging in the appropriate extension of the Hotelling test. Using a simulation study, we show that the proposed test is advantageous over state-of-the-art tests in many scenarios and robust to violation of the Gaussian assumption.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-021-00781-z