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Obtaining remainder term estimates by an inversion technique

Published online by Cambridge University Press:  01 July 2016

Gunnar Englund
Gunnar Englund*
Affiliation:
Royal Institute of Technology, Stockholm
*
∗Postal address: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
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Abstract

Let be a double sequence of random variables such that there exists a ‘dual' sequence satisfying , and that can be expressed as a sum of independent random variables. If (suitably centered and rescaled) is approximately normally distributed as k and N → ∞ in some fashion, we can use this fact to obtain a remainder-term estimate for the asymptotic normality of as n and N → ∞ in some prescribed manner. The result in the general theorem is used in two specific situations: (i) classical occupancy where the balls can fall through the boxes, (ii) a capture-recapture problem where tagging affects catchability.

Keywords

CENTRAL LIMIT THEOREMCLASSICAL OCCUPANCYCAPTURE–RECAPTURE PROBLEMS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 1 , March 1984 , pp. 88 - 110
Copyright
Copyright © Applied Probability Trust 1984 

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