Application of the empirical Bayes approach to nonparametric testing for high-dimensional data

Abstract

In [5] a simple, data-driven and computationally efficient procedure of (nonparametric) testing for high-dimensional data have been introduced. The procedure is based on randomization and resampling, a special sequential data partition procedure, and χ²-type test statistics. However, the χ² test has small power when deviations from the null hypothesis are small or sparse. In this note test statistics based on the nonparametric maximum likelihood and the empirical Bayes estimators.