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May, 1979 Two Conditional Limit Theorems with Applications
Lars Holst
Ann. Statist. 7(3): 551-557 (May, 1979). DOI: 10.1214/aos/1176344676


Let $(X_1, Y_1),\cdots, (X_N, Y_N)$ be i.i.d. rv's where the $X$'s are nonnegative integer-valued. Conditional on $\sigma X_k$ the asymptotic distribution of $\sigma Y_k$ and $\sigma a_k X_k$ are derived by general methods. Some applications are briefly discussed: sampling without replacement, the classical occupancy problem, the Wilcoxon statistic, the Poisson index of dispersion, testing geometric versus Poisson distribution.


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Lars Holst. "Two Conditional Limit Theorems with Applications." Ann. Statist. 7 (3) 551 - 557, May, 1979.


Published: May, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0406.62008
MathSciNet: MR527490
Digital Object Identifier: 10.1214/aos/1176344676

Primary: 62E20
Secondary: 60F05

Keywords: conditioning with sufficient statistics , limit theorems , nonparametrics , occupancy problems , sampling without replacement , testing fit of Poisson distribution , urn models

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 3 • May, 1979
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