Corrected-Hill versus partially reduced-bias value-at-risk estimation

M. Ivette Gomes, Frederico Caeiro, Fernanda Figueiredo, Lígia Henriques-Rodrigues, Dinis Pestana

Research output: Contribution to journalArticle

1 Citation (Scopus)


The value-at-risk (VaR) at a small level q, 0<q<1, is the size of the loss that occurs with a probability q. Semi-parametric partially reduced-bias (PRB) VaR-estimation procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p any real number, are put forward. After the study of their asymptotic behavior, these PRB VaR-estimators are altogether compared with the classical ones for finite samples, through a large-scale Monte-Carlo simulation study. A brief application to financial log-returns is provided, as well as some final remarks.

Original languageEnglish
JournalCommunications in Statistics: Simulation and Computation
Publication statusAccepted/In press - 1 Jan 2019



  • Heavy right tails
  • Heuristic sample fraction selection; Monte-Carlo simulation; Semi-parametric estimation; Statistics of extremes; Value-at-risk estimation
  • Primary 62G32; Secondary 65C05

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