Asymptotically achievable error probabilities for multiple hypothesis testing

The region of achievable error probabilities for k-ary hypothesis tests is studied in the asymptotic setting with n independent and identically distributed observations. We identify a k
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- k - 1 dimensional parametric family of optimal (non-dominated) tests and relate it to a family of Bayes tests whose loss function depends exponentially on n. We asymptotically characterize the conditional error probabilities for these tests within O(1) as n → ∞, using strong large deviations analysis.