Abstract
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> 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.
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