In  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.
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