Box–Cox transformations and heavy-tailed distributions

It is a stylized fact that estimators in extreme-value theory suffer from serious bias. Moreover, graphical representations of extremal data often show erratic behaviour. In the statistical literature it is advised to use a Box–Cox transformation in order to make data more suitable for statistical a...

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Bibliographic Details
Published in:Journal of applied probability 2004, Vol.41 (A), p.213-227
Main Authors: Teugels, Jef L., Vanroelen, Giovanni
Format: Article
Language:English
Subjects:
26A12
60G70
62G32
Box-Cox transformation
Estimation bias
Estimators
Heavy-Tail Analysis
heavy-tailed distributions
Hill estimator
Mathematical functions
Mathematical transformations
Part 4. Heavy-tail analysis
Random sampling
Random variables
Sampling distributions
second-order regular variation
Statistical variance
Statistics
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Summary:It is a stylized fact that estimators in extreme-value theory suffer from serious bias. Moreover, graphical representations of extremal data often show erratic behaviour. In the statistical literature it is advised to use a Box–Cox transformation in order to make data more suitable for statistical analysis. We provide some of the theoretical background to see the effect of such transformations and to investigate under what circumstances they might be helpful.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1082552200