## Global and local two-sample tests via regression.(English)Zbl 1435.62199

The objective of this paper is to report on global and local tests to determine if two samples are from different multivariate distributions. Such tests have applications in a variety of machine learning areas, e.g. to detect differences in healthy and cancerous tissue, in database attribute matching and many other classification and regression problems. Under condition that two populations only differ in their means it is proved that the regression test based on Fisher’s LDA achieves the same local optimality as the Hotelling’s $$T^2$$ test. The simulation studies are fulfilled to examine the empirical performance of the proposed tests. The empirical performance of proposed tests is validated at the datasets from Hubble Space Telescope: it is shown that the proposed approach can identify galaxies with specific features of star-forming galaxies.

### MSC:

 62H15 Hypothesis testing in multivariate analysis 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 85A15 Galactic and stellar structure 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62J05 Linear regression; mixed models 62P35 Applications of statistics to physics 62H35 Image analysis in multivariate analysis

GeneSrF; hypoRF
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### References:

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