Chapter

The Classical Central Limit Theorem

James Davidson

in Stochastic Limit Theory

Published in print October 1994 | ISBN: 9780198774037
Published online November 2003 | e-ISBN: 9780191596117 | DOI: http://dx.doi.org/10.1093/0198774036.003.0023

Series: Advanced Texts in Econometrics

 The Classical Central Limit Theorem

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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

Chapter.  8695 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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