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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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The Classical Central Limit Theorem

The Classical Central Limit Theorem

Chapter:
(p.364) 23 The Classical Central Limit Theorem
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0023

In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg‐Lévy, Khinchine, Lindeberg‐Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances

Keywords:   asymptotic negligibility, Khinchine's theorem, Liapunov theorem, Lindeberg condition, Lindeberg‐Feller theorem, Lindeberg‐Lévy theorem, trending variances

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