Extreme Value Analysis based on Blockwise Top-Two Order Statistics

TL;DR

This paper introduces a new bias-corrected estimator for extreme value analysis based on blockwise top-two order statistics, improving efficiency over traditional methods in environmental time series applications.

Contribution

It proposes a novel, consistent estimator using blockwise large order statistics, addressing bias issues in classical extreme value analysis methods.

Findings

The new estimator is more efficient than traditional methods.

It provides accurate estimates of large return levels and periods.

The estimator is validated through theoretical analysis and simulations.

Abstract

Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of (annual) block maxima. Mathematically, the target parameters of the extreme-value distribution also show up in limit results for other high order statistics, which suggests estimation based on blockwise large order statistics. It is shown that a naive approach based on maximizing an independence log-likelihood yields an estimator that is inconsistent in general. A consistent, bias-corrected estimator is proposed, and is analyzed theoretically and in finite-sample simulation studies. The new estimator is shown to be more efficient than traditional counterparts, for instance for estimating large return levels or return periods.