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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

(p.399) 25 Some Extensions
Stochastic Limit Theory

James Davidson

Oxford University Press

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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