  We consider a standard binary classification problem. The performance of any
binary classifier based on the training data is characterized by the excess
risk. We study Bahadur's type exponential bounds on the minimax accuracy
confidence function based on the excess risk. We study how this quantity
depends on the complexity of the class of distributions characterized by
exponents of entropies of the class of regression functions or of the class of
Bayes classifiers corresponding to the distributions from the class. We also
study its dependence on margin parameters of the classification problem.
