New error bounds with the nearest neighbor rule (Corresp.)

A distribution-free lower bound on the Bayes error rate is formulated in terms of the asymptotic error rate of the nearest neighbor rule with a reject option. Next, a closed form expression for an upper bound of the th nearest neighbor error rate in terms of the Bayes rate is established. These results are discussed in the framework of recent works on nonparametric estimation of the Bayes error rate.