Extreme values identification in regression using a peaks-over-threshold approach

Abstract

The problem of heavy tail in regression models is studied. It is proposed that regression models are estimated by a standard procedure and a statistical check for heavy tail using residuals is conducted as a tool for regression diagnostic. Using the peaks-over-threshold approach, the generalized Pareto distribution quantifies the degree of heavy tail by the extreme value index. The number of excesses is determined by means of an innovative threshold model which partitions the random sample into extreme values and ordinary values. The overall decision on a significant heavy tail is justified by both a statistical test and a quantile–quantile plot. The usefulness of the approach includes justification of goodness of fit of the estimated regression model and quantification of the occurrence of extremal events. The proposed methodology is supplemented by surface ozone level in the city center of Leeds.

Keywords:

• exponential threshold model
• extreme value index
• ozone
• peaks-over-threshold
• regression diagnostic

AMS Subject Classifications::

• 62J05
• 62J20
• 62N02
• 62N03
• 62P12

Acknowledgments

We are grateful to the Editor and reviewers for their constructive comments and suggestions for improvements.