The Annals of Statistics

Two Conditional Limit Theorems with Applications

Lars Holst

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Abstract

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.

Article information

Source
Ann. Statist., Volume 7, Number 3 (1979), 551-557.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344676

Digital Object Identifier
doi:10.1214/aos/1176344676

Mathematical Reviews number (MathSciNet)
MR527490

Zentralblatt MATH identifier
0406.62008

JSTOR
links.jstor.org

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

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

Citation

Holst, Lars. Two Conditional Limit Theorems with Applications. Ann. Statist. 7 (1979), no. 3, 551--557. doi:10.1214/aos/1176344676. https://projecteuclid.org/euclid.aos/1176344676


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