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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

(p.364) 23 The Classical Central Limit Theorem
Stochastic Limit Theory

James Davidson

Oxford University Press

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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