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Asymptotic expansions of the probabilities of misclassification for k-NN discriminant rules

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  • Chanda, Kamal C.

Abstract

Let X1,..., Xl and Y1,..., Yn be independent random samples from the distributions functions (d.f.) F and G respectively. Assume that F' = f and G' = g. The discriminant rule for classifying an independently sampled observation z to F if (z) > (z), and to G otherwise where and are the nearest neighbor estimates of f and g respectively based on the 'training' X- and Y-samples is considered optimal in some sense. Let PF denote the probability measure under the assumption that Z ~ F and set P0 = PF(f(Z) P0 as l, n --> [infinity], for the situation where l = n, F(x) = M(x - [theta]2) and G(x) = M(x - [theta]1) for some symmetric d.f. M with a compact support and parameters [theta]1, [theta]2. It is also established through an example that this rate of convergence does not necessarily hold if the support of the symmetric d.f. M is infinite.

Suggested Citation

  • Chanda, Kamal C., 1990. "Asymptotic expansions of the probabilities of misclassification for k-NN discriminant rules," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 341-349, September.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:4:p:341-349
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