Rate of convergence of local averaging plug-in classification rules under margin condition

We discuss rates of convergence of plug-in kernel, partitioning and nearest neighbors classification rules under margin condition. Margin condition characterizes the rate with which a posteriori probabilities cross the decision boundary. We show the rates of convergence of the plug-in classifiers under smoothness conditions on a posteriori probabilities and assuming that feature vectors are contained in a compact set. We obtain particularly fast rates of convergence assuming, in addition, that feature vectors distributions have densities bounded away from zero