Statistica Sinica 25 (2015), 1421-1435

ON SOME EXACT DISTRIBUTION-FREE ONE-SAMPLE

TESTS FOR HIGH DIMENSION LOW SAMPLE SIZE DATA

Munmun Biswas, Minerva Mukhopadhyay and Anil K. Ghosh

Indian Statistical Institute, Kolkata

Abstract: Several rank-based tests for the multivariate one-sample problem are available in the literature. But, unlike univariate rank-based tests, most of these multivariate tests are not distribution-free. Moreover, many of them are not applicable when the dimension of the data exceeds the sample size. We develop and investigate some distribution-free tests for the one-sample location problem, which can be conveniently used in high dimension low sample size (HDLSS) situations. Under some appropriate regularity conditions, we prove the consistency of these tests when the sample size remains fixed and the dimension grows to infinity. Some simulated and real data sets are analyzed to compare their performance with popular one-sample tests.

Key words and phrases: HDLSS data, linear rank tests, run tests, shortest covering path, weak law of large numbers.