Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T23:59:21.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Remainder term estimates in a conditional central limit theorem for integer-valued random variables

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

M. P. Quine
M. P. Quine
Affiliation:
Department of Mathematical StatisticsUniversity of SydneySydney, N.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Berry-Esseen type result is given for the conditional distribution of a weighted sum of i.i.d. integer-valued r.v.'s given that their unweighted sum equals its expectation. The examples include the case of sampling without replacement from a finite population.

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 75 - 85
Copyright
Copyright © Australian Mathematical Society 1985

References

Abramowitz, M. and Stegun, I. A. (1965), Handbook of mathematical functions (Dover, New York).Google Scholar
Bartlett, M. S. (1938), ‘The characteristic function of a conditional statistic’, J. London Math. Soc. 13, 62–67.CrossRefGoogle Scholar
Bhattacharya, R. N. and Rao, R. Ranga (1976), Normal approximation and asymptotic expansions (Wiley, New York).Google Scholar
Gnedenko, B. V. (1962), The theory of probability (Chelsea, New York).Google Scholar
Höglund, T. (1976), ‘Sampling from a finite population: a remainder term estimate’, Studia Sd. Math. Hungar. 11, 69–74.Google Scholar
Holst, L. (1979), ‘Two conditional limit theorems with applications’, Ann. Statist. 1, 551–557.Google Scholar