On the finite sample performance of the nearest neighbor classifier

Abstruct-The finite sample performance of a nearest neighbor classifier is analyzed for a two-class pattern recognition problem. An exact integral expression is derived for the m-sample risk R, given that a reference m-sample of labeled points is available to the classifier. The statistical setup assumes that the pattern classes arise in nature with fixed a priori probabilities and that points representing the classes are drawn from Euclidean n-space according to fixed class-conditional probability distributions. The sample is assumed to consist of m independently generated class-labeled points. For a family of smooth classconditional distributions characterized by asymptotic expansions in general form, it is shown that the m-sample risk R,,, has a complete asymptotic series expansion