What is it about?
The multivariate comparison problem is addressed. High-dimensional data are increasingly encountered when analyzing medical and biological problems, and in these situations the familiar Hotelling test performs poorly or cannot be computed. A test that is unbiased for non-normal data, for small sample sizes as well as for two-sided alternatives and that can be computed for high-dimensional data has been recently proposed and is based on the ranks of the interpoint Euclidean distances between observations. Five modifications of this test are proposed. Unbiasedness and consistency of the tests are proven and the problem of power computation is addressed. It is shown that two of the modified interpoint distance-based tests are always more powerful than the original test. They are suggested when the assumption of normality is not tenable and/or in case of high-dimensional data with complex dependence structure which are typical in molecular biology and medical imaging.
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Why is it important?
Much better alternatives to the Hotelling test are proposed.
Perspectives
Very powerful and robust methods to address high-dimensional low-sample size case-control studies are proposed. These settings are increasingly encountered when analyzing medical and biological problems.
Dr Marco Marozzi
Ca' Foscari University of Venice
Read the Original
This page is a summary of: Multivariate tests based on interpoint distances with application to magnetic resonance imaging, Statistical Methods in Medical Research, July 2016, SAGE Publications,
DOI: 10.1177/0962280214529104.
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