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Let be a random element in a metric space , and let be a random variable with value or . is called the class, or the label, of . Let ( be an observed i.i.d. sample having the same law as . The problem of classification is to predict the label of a new random element . The -nearest neighbor classifier is the simple following rule: look at the nearest neighbors of in the trial sample and choose or for its label according to the majority vote. When $(ℱ,d)=({ℝ}^d,||.|\left|\right)$, Stone (1977) proved in 1977 the universal...