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- W1981565774 abstract "Let X1,…, X1 and Y1,…, Yn be independent random samples from the distribution functions (d.f.) F and G respectively. Assume that F′ = f and G′ = g. The discriminant rule for classifying and independently sampled observation Z to F if fl(z) > gn(z) and to G, otherwise where fl and gn are the estimates of f and g respectively based on a common kernel function and the training X- and Y-samples, are considered optimal in some sense. Let Pf denote the probability measure under the assumption that Z ∼ F and set P0 = Pf(f(Z) > g(Z)) and Pn = Pf(fl(Z) > gn(Z)). In this article we have derived the rate at which PN → P0 as N = l + n → ∞, for the situation where l = n, F(x) = TM(x − θ2) and G(x) = M(x − θ1) for some symmetric d.f. M and parameters θ1, θ2. We have examined a few special cases of M and have established that the rate of convergence of PN to P0 depends critically on the tail behavior of m = M′." @default.
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- W1981565774 date "1989-05-01" @default.
- W1981565774 modified "2023-09-29" @default.
- W1981565774 title "Asymptotic estimate of probability of misclassification for discriminant rules based on density estimates" @default.
- W1981565774 cites W4238472918 @default.
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- W1981565774 doi "https://doi.org/10.1016/0167-7152(89)90088-6" @default.
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