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

Tong Siu Tung WONG, Wai Keung LI

Research output: Contribution to journalArticles

2 Citations (Scopus)

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. Copyright © 2014 Taylor & Francis.
Original languageEnglish
Pages (from-to)566-576
JournalJournal of Applied Statistics
Volume42
Issue number3
Early online dateNov 2014
DOIs
Publication statusPublished - 2015

Citation

Wong, T. S. T., & Li, W. K. (2015). Extreme values identification in regression using a peaks-over-threshold approach. Journal of Applied Statistics, 42(3), 566-576. doi: 10.1080/02664763.2014.978843

Keywords

  • Exponential threshold model
  • Extreme value index
  • Ozone
  • Peaks-over-threshold
  • Regression diagnostic

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