Binary Hypothesis Testing with Learning of Empirical Distributions

Binary hypothesis testing with a single observer is considered. The true distributions of the observations under either hypothesis are unknown. Empirical distributions are estimated from observations. A sequence of detection problems are solved using the sequence of empirical distributions. The convergence of the information state and optimal detection cost under empirical distributions to the information state and optimal detection cost under the true distribution are shown. Simulation results are presented and are consistent with the results mentioned earlier. Copyright (C) 2021 The Authors.