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A Normal Limit Law for a Nonparametric Estimator of the Coverage of a Random Sample

Warren W. Esty
The Annals of Statistics
Vol. 11, No. 3 (Sep., 1983), pp. 905-912
Stable URL: http://www.jstor.org/stable/2240652
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Normal Limit Law for a Nonparametric Estimator of the Coverage of a Random Sample
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Abstract

The coverage of a multinomial random sample is the sum of the probabilities of the observed classes. A normal limit law is rigorously proved for Good's (1953) coverage estimator. The result is valid under very general conditions and all terms except the coverage itself are observable. Nevertheless the implied confidence intervals are not much wider than those developed under restrictive assumptions such as in the classical occupancy problem. The asymptotic variance is somewhat unexpected. The proof utilizes a method of Holst (1979).

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