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Exact convergence rate and leading term in central limit theorem for student's t statistic

Hall, Peter; Wang, Qiying


The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation is used to give the exact rate of convergence in the central limit theorem up to order n⁻¹/²,...[Show more]

CollectionsANU Research Publications
Date published: 2004-10-06
Type: Journal article
Source: Annals of Probability
DOI: 10.1214/009117904000000252


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