Approximation of high quantiles from intermediate quantiles

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• 作者：Cees de Valk
• 关键词：Extreme value theory ; Quantile estimation ; High quantile ; Generalised Weibull tail limit ; log ; GW tail limit ; Weibull tail limit ; Extended regular variation
• 刊名：Extremes
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：19
• 期：4
• 页码：661-686
• 全文大小：695 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Quality Control, Reliability, Safety and Risk
  Civil Engineering
  Hydrogeology
  Environmental Management
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer U.S.
• ISSN：1572-915X
• 卷排序：19

文摘

Motivated by applications requiring quantile estimates for very small probabilities of exceedance p_n≪1/n, this article addresses estimation of high quantiles for p_n satisfying \(p_{n}\in [n^{-\tau _{2}},n^{-\tau _{1}}]\) for some τ₁>1 and τ₂>τ₁. For this purpose, the tail regularity assumption logU∘ exp∈ERV (with U the left-continuous inverse of 1/(1−F), and ERV the extended regularly varying functions) is explored as an alternative to the classical regularity assumption U∈ERV (corresponding to the Generalised Pareto tail limit). Motivation for the alternative regularity assumption is provided, and it is shown to be equivalent to a limit relation for the logarithm of the survival function, the log-GW tail limit, which generalises the GW (Generalised Weibull) tail limit, a generalisation of the Weibull tail limit. The domain of attraction is described, and convergence results are presented for quantile approximation and for a simple quantile estimator based on the log-GW tail. Simulations are presented, and advantages and limitations of log-GW-based estimation of high quantiles are indicated.