e consider the problem of detecting sparse heterogeneous mixtures from
a nonparametric perspective. Specifically, we assume that the null distribution is sym-
metric about zero, while the true effects have positive median. We then suggest two
new tests for this purpose. The main one is a form of Anderson–Darling test for sym-
metry and is closely related to the higher criticism. It is shown to achieve the detection
boundary for the normal mixture model and, more generally, for asymptotically gen-
eralized Gaussian mixture models, in all sparsity regimes. The other test is a form of
longest run test and specifically designed for the very sparse situation.

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