  When the competing classes in a classification problem are not of comparable
size, many popular classifiers exhibit a bias towards larger classes, and the
nearest neighbor classifier is no exception. To take care of this problem, we
develop a statistical method for nearest neighbor classification based on such
imbalanced data sets. First, we construct a classifier for the binary
classification problem and then extend it for classification problems involving
more than two classes. Unlike the existing oversampling or undersampling
methods, our proposed classifiers do not need to generate any pseudo
observations or remove any existing observations, hence the results are exactly
reproducible. We establish the Bayes risk consistency of these classifiers
under appropriate regularity conditions. Their superior performance over the
existing methods is amply demonstrated by analyzing several benchmark data
sets.
