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Obtaining remainder term estimates by an inversion technique
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- Journal:
- Advances in Applied Probability / Volume 16 / Issue 1 / March 1984
- Published online by Cambridge University Press:
- 01 July 2016, pp. 88-110
- Print publication:
- March 1984
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- Article
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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.
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 
as 