Kernel regression with Weibull-type tails

Tertius de Wet, Yuri Goegebeur, Armelle Guillou, Michael Osmann

Research output: Contribution to journalJournal articleResearchpeer-review


We consider the estimation of the tail coefficient of a Weibull-type distribution in the presence of random covariates. The approach followed is non-parametric and consists of locally weighted estimation in narrow neighbourhoods in the covariate space. We introduce two families of estimators and study their asymptotic behaviour under some conditions on the conditional response distribution, the kernel function, the density function of the independent variables, and for appropriately chosen bandwidth and threshold parameters. We also introduce a Weissman-type estimator for estimating upper extreme conditional quantiles. The finite sample behaviour of the proposed estimators is examined with a simulation experiment. The practical applicability of the methodology is illustrated on a dataset of sea storm measurements.

Original languageEnglish
JournalAnnals of the Institute of Statistical Mathematics
Issue number5
Pages (from-to)1135-1162
Publication statusPublished - 2016


  • Extreme value statistics
  • Regression
  • Second-order condition
  • Weibull-type distribution


Dive into the research topics of 'Kernel regression with Weibull-type tails'. Together they form a unique fingerprint.

Cite this