Statistics of heteroscedastic extremes

John Einmahl, L.F.M. de Haan, C. Zhou

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)

Abstract

We extend classical extreme value theory to non-identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown; they are asymptotically independent. We also establish asymptotic normality of a forecasted high quantile and develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of the procedures and also present an application to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.
Original languageEnglish
Pages (from-to)31-51
Number of pages21
JournalJournal of the Royal Statistical Society, Series B
Volume78
Issue number1
DOIs
Publication statusPublished - Jan 2016

Keywords

  • Extreme value statistics
  • functional limit theorems
  • non-identical distributions
  • sequential tail empirical process

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