Some high-dimensional one-sample tests based on functions of interpoint distances

The multivariate one-sample location problem is well studied in the literature, and several tests are available for it. But most of the existing tests perform poorly for high dimensional data, and many of them are not applicable when the dimension exceeds the sample size. In this article, we develop and investigate some nonparametric one-sample tests based on functions of interpoint distances. These proposed tests can be conveniently used in high dimension low sample size (HDLSS) situations, and good power properties of these tests for HDLSS data have been established using both theoretical as well as numerical results.