Novel tight classification error bounds under mismatch conditions based on f-Divergence

By default, statistical classification/multiple hypothesis testing is faced with the model mismatch introduced by replacing the true distributions in Bayes decision rule by model distributions estimated on training samples. Although a large number of statistical measures exist w.r.t. to the mismatch introduced, these works rarely relate to the mismatch in accuracy, i.e. the difference between model error and Bayes error. In this work, the accuracy mismatch between the ideal Bayes decision rule/Bayes test and a mismatched decision rule in statistical classification/multiple hypothesis testing is investigated explicitly. A proof of a novel generalized tight statistical bound on the accuracy mismatch is presented. This result is compared to existing statistical bounds related to the total variational distance that can be extended to bounds of the accuracy mismatch. The analytic results are supported by distribution simulations.