Unification of Rare and Weak Multiple Testing Models using Moderate Deviations Analysis and Log-Chisquared P-values

Rare and Weak models for multiple hypothesis testing assume that only a small proportion of the tested hypotheses concern non-null effects individual are moderately large, so they generally do not stand out individually, example in Bonferroni analysis. Such have been studied quite few settings, some cases studies focused on an underlying Gaussian means model being tested; others, Poisson Binomial. seemingly different asymptotically following common structure. Summarizing evidence tests by negative logarithm its P-value, is equivalent to situation which most log P-values standard exponential distribution but fraction might alternative approximately noncentral chisquared one degree freedom. This log-chisquared approximation from log-normal Bahadur unsuitable analyzing models. We characterize asymptotic performance global combining terms mixture parameters: scaling parameter controlling heteroscedasticity, non-centrality describing effect size whenever it exists, rarity effects. In phase space involving last two parameters, we derive region where all powerless. Outside this region, Berk-Jones Higher Criticism maximal power. Inference techniques based minimal false-discovery rate controlling, Fisher's combination test sub-optimal diagrams.