Empirical Bayes testing goodness-of-fit for high-dimensional data

In [6] a simple, data-driven and computationally e±cient procedure of (non- parametric) testing for high-dimensional data have been introduced. The proce- dure is based on randomization and resampling, a special sequential data par- tition procedure, and В2-type test statistics. However, the В2 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 empiri- cal Bayes estimators in an auxiliary nonparametric mixture model are proposed instead