Testing against a high dimensional alternative

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Hierarchical testing of variable importance (2008, methodology): “In Figure 3, the power is shown as a function of cluster size for three mentioned tests of collective effects: the F-test, Higher Criticism of Donoho and Jin (2004) and the Score test proposed by Goeman et al. (2005).”
Controlling false positive selections in high-dimensional regression and causal inference (2013, background): “large-scale multiple testing of many marginal parameters(12) or global tests.(13) For non-marginal parameters such as regression coefficients or causal effects one can rely on subsampling or sample-splitting: we review and discuss stability”
Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control (2011, methodology): “The test based on Ŝ can be used when the dimensionality of the alternative hypothesis is very large and can then be quite powerful (Goeman et al., 2006).”
Breaking the curse of dimensionality in regression (2017, background): “The case of sparse alternatives have been considered in Goeman et al. (2006) where the authors show optimality over an average of high-dimensional alternatives of an empirical Bayes test of the form Y>WW>Y/‖Y‖22.”