HDLSSkST: Distribution-Free Exact High Dimensional Low Sample Size k-Sample Tests

We construct four new exact level (size) alpha tests for testing the equality of k distributions, which can be conveniently used in high dimensional low sample size setup based on clustering. These tests are easy to implement and distribution-free. Under mild conditions, we have proved the consistency of these tests as the dimension d of each observation grows to infinity, whereas the sample size remains fixed. We also apply step-down-procedure (1979) for multiple testing. Details are in Biplab Paul, Shyamal K De and Anil K Ghosh (2020); Soham Sarkar and Anil K Ghosh (2019) <doi:10.1109/TPAMI.2019.2912599>; William M Rand (1971) <doi:10.1080/01621459.1971.10482356>; Cyrus R Mehta and Nitin R Patel (1983) <doi:10.2307/2288652>; Joseph C Dunn (1973) <doi:10.1080/01969727308546046>; Sture Holm (1979) <doi:10.2307/4615733>.

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