k-nearest-neighbor Bayes-risk estimation

Abstract

Nonparametric estimation of the Bayes riskR^\astusing ak-nearest-neighbor (k-NN) approach is investigated. Estimates of the conditional Bayes errorr(X)for use in an unclassified test sample approach to estimateR^\astare derived using maximum-likelihood estimation techniques. By using the volume information as well as the class representations of thek-NN's toX, the mean-squared error of the conditional Bayes error estimate is reduced significantly. Simulations are presented to indicate the performance of the estimates using unclassified testing samples.