A competitive Neyman-Pearson approach to universal hypothesis testing with applications

摘要

A new generalization of the Neyman-Pearson approach to the problem of composite hypothesis testing is proposed. The resulting universal test is shown to be efficient in the sense of achieving exponential decay of both types of error for all values of unknown parameters, whenever such an efficient universal test exists. The best universally achievable error exponents are identified and conditions for the existence of efficient universal tests are established.