Strong large deviations for composite hypothesis testing
Yen-Wei Huang, Pierre Moulin · 2014
A simple hypothesis P is tested against a composite hypothesis ℚj, j ∈ {1,2, ...,k}, each ℚjbeing a product of n probability distributions. We consider the set of achievable false-positive error probability vectors for a generalized Neyman-Pearson test under a constraint on the probability of correct detection under P. Exact asymptotics (as n → ∞) are derived for this set, in particular the set is determined within an O(1) term.