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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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Some Extensions

Some Extensions

Chapter:
(p.399) 25 Some Extensions
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0025

Four extensions of the CLT are considered in this chapter. First, estimated normalization, using methods of heteroscedasticity and autocorrelation consistent variance estimation. Second, random norming, giving rise to a mixed Gaussian limiting distribution. Third, the Cramér‐Wold device, and the extension to the multivariate CLT. Lastly, error estimation and the law of the iterated logarithm.

Keywords:   autocorrelation, Berry‐Esséen theorem, Cramér‐Wold device, Hartman‐Wintner theorem, heteroscedasticity, iterated logarithm, kernel estimation, mixed Gaussian distribution, random norming

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