The Annals of Statistics

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

Warren W. Esty

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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).

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 905-912.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346256

Digital Object Identifier
doi:10.1214/aos/1176346256

Mathematical Reviews number (MathSciNet)
MR707940

Zentralblatt MATH identifier
0599.62053

JSTOR
links.jstor.org

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory

Keywords
Coverage total probability occupancy problem cataloging problem unobserved species urn models

Citation

Esty, Warren W. A Normal Limit Law for a Nonparametric Estimator of the Coverage of a Random Sample. Ann. Statist. 11 (1983), no. 3, 905--912. doi:10.1214/aos/1176346256. https://projecteuclid.org/euclid.aos/1176346256


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