A nearest-neighbor-based ensemble classifier and its large-sample optimality

A nonparametric approach is proposed to combine several individual classifiers in order to construct an asymptotically more accurate classification rule in the sense that its misclassification error rate is, asymptotically, at least as low as that of the best individual classifier. The proposed method uses a nearest neighbour type approach to estimate the conditional expectation of the class associated with a new observation (conditional on the vector of individual predictions). Both mechanics and the theoretical validity of the proposed approach are discussed. As an interesting by product of our results, it is shown that the proposed method can also be applied to any single classifier in which case the resulting new classifier will be at least as good as the original one. Several numerical examples, involving both real and simulated data, are also given. These numerical studies further confirm the superiority of the proposed classifier.