CONSTANT VERSUS COVARIATE DEPENDENT THRESHOLD IN THE PEAKS-OVER THRESHOLD METHOD

Richard Minkah, Tertius de Wet

Research output: Contribution to journalArticlepeer-review

Abstract

The Peaks-Over Threshold is a fundamental method in the estimation of rare events such as extreme quantiles. The main problem with the Peaks-Over Threshold method is the selection of threshold above which the asymptotic results are valid for large observations. Also, the main assumption leading to the asymptotic results is that the observations are independent and identically distributed. However, in practice, many real-life processes yield data that may be related to some covariate variables. Strong arguments have been made against the use of constant threshold as an observation that is considered extreme at some covari-ate level may not qualify as an extreme observation at another covariate level. In this paper, we propose a covariate dependent threshold based on expectiles. The expectile threshold better spans the covariate space in contrast to the constant threshold and an existing covariate dependent threshold based on quantile regression. We compare the expectile threshold with the constant and quantile regression thresholds in a simulation study involving an exponential growth data for estimating the tail index of the Generalised Pareto distribution. As may be expected, no threshold selection method is universally the best. However, the proposed expectile threshold outperforms the others when the response variable has smaller to medium values in an exponential growth data. For larger values of the response variable, the constant threshold is generally the best method. We illustrate the threshold selection methods in estimating the tail index of an insurance claim data set.

Original languageEnglish
Pages (from-to)27-48
Number of pages22
JournalJournal of Applied Probability and Statistics
Volume15
Issue number3
Publication statusPublished - Dec 2020

Keywords

  • Covariates
  • Maximum Likelihood
  • Peaks-Over Threshold
  • Simulation
  • Tail Index
  • Thresholds

Fingerprint

Dive into the research topics of 'CONSTANT VERSUS COVARIATE DEPENDENT THRESHOLD IN THE PEAKS-OVER THRESHOLD METHOD'. Together they form a unique fingerprint.

Cite this