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
k
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.