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- W2315693524 abstract "Given an i.i.d. sequence X 1 , X 2 , … with common distribution function (d.f.) F, the usual non-parametric estimator of F is the e.d.f. F n ; where U o is the d.f. of the unit mass at zero. An admissible perturbation of the e.d.f. , say , is obtained if U o is replaced by a d.f. , where is a sequence of d.f.'s converging weakly to U o . Such perturbed e.d.f.′ s arise quite naturally as integrals of non-parametric density estimators, e.g. as . It is shown that if F satisfies some smoothness conditions and the perturbation is not too drastic then ‘has the Chung–Smirnov property'; i.e., with probability one, 1. But if the perturbation is too vigorous then this property is lost: e.g., if F is the uniform distribution and H n is the d.f. of the unit mass at n –α then the above lim sup is ≦ 1 or = ∞, depending on whether or" @default.
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- W2315693524 date "1979-03-01" @default.
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- W2315693524 title "Convergence rate of perturbed empirical distribution functions" @default.
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- W2315693524 doi "https://doi.org/10.2307/3213384" @default.
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