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Box–Cox transformations and heavy-tailed distributions

Part of: Nonparametric inference Stochastic processes Real functions

Published online by Cambridge University Press:  14 July 2016

Jef L. Teugels  and
Giovanni Vanroelen
Jef L. Teugels
Affiliation:
University Statistics Centre (UCS), Katholieke Universiteit Leuven, W. De Croylaan 54, 3001 Leuven, Belgium. Email address: jef.teugels@wis.kuleuven.ac.be
Giovanni Vanroelen
Affiliation:
University Statistics Centre (UCS), Katholieke Universiteit Leuven, W. De Croylaan 54, 3001 Leuven, Belgium. Email address: giovanni.vanroelen@wis.kuleuven.ac.be
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Abstract

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.

Keywords

Box–Cox transformationsecond-order regular variationHill estimatorheavy-tailed distributions

MSC classification

Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions
Secondary: 62G32: Statistics of extreme values; tail inference 60G70: Extreme value theory; extremal processes
Type
Part 4. Heavy-tail analysis
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 213 - 227
Copyright
Copyright © Applied Probability Trust 2004 

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