Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem

Jun Li

Biometrika, 2018, vol. 105, issue 3, 529-546

Abstract: SummaryInterpoint distances have applications in many areas of probability and statistics. Thanks to their simplicity of computation, interpoint distance-based procedures are particularly appealing for analysing small samples of high-dimensional data. In this paper, we first study the asymptotic distribution of interpoint distances in the high-dimension, low-sample-size setting and show that it is normal under regularity conditions. We then construct a powerful test for the two-sample problem, which is consistent for detecting location and scale differences. Simulations show that the test compares favourably with existing distance-based tests.

Keywords: Asymptotic normality; High-dimensional data; Interpoint distance; Strong mixing condition; Two-sample problem (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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