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It is shown in the classification problem, when independent samples are taken from uniform distributions, that for small sample sizes the probability of misclassification when using the nearest-neighbor rule is "close" to its asymptotic value. It is also shown that when using this rule the probability of classification in many cases is close to its Bayes optimum even for small sample sizes. Moreover, if one is restricted to a small sample size from one population, it is shown that it is not necessary to "make up" this deficiency by taking a large sample from the other population; best results may be obtained when both sample sizes are small.
Date of Publication: Sep 1973