The asymptotic behavior of threshold-based classification rules constructed from a sample from a mixture with varying concentrations

摘要

We consider a problem on finding the best threshold-based classification rule constructed from a sample from a mixture with varying concentrations. We show that the rate of convergence of the minimal empirical risk estimators to the optimal threshold is of order N~(-1/3) for smooth distributions, while the rate of convergence of the Bayes empirical estimators is of order N~(-2/5) where N is the size of a sample.