Parameter estimation for the generalized extreme value distribution: a method that combines bootstrapping and r largest order statistics

TL;DR

This paper introduces a novel parameter estimation method for the generalized extreme value distribution that combines the r largest order statistics approach with permutation bootstrapping, improving accuracy over existing methods.

Contribution

It proposes a new estimation technique integrating r-LOS with bootstrapping, enhancing parameter estimation in extreme value theory.

Findings

Estimates are more accurate with combined r-LOS and bootstrapping.

Method outperforms individual approaches in synthetic and real data.

Improves reliability of extreme value distribution parameter estimates.

Abstract

A critical problem in extreme value theory (EVT) is the estimation of parameters for the limit probability distributions. Block maxima (BM), an approach in EVT that seeks estimates of parameters of the generalized extreme value distribution (GEV), can be generalized to take into account not just the maximum realization from a given dataset, but the r largest order statistics for a given r. In this work we propose a parameter estimation method that combines the r largest order statistic (r-LOS) extension of BM with permutation bootstrapping: surrogate realizations are obtained by randomly reordering the original data set, and then r-LOS is applied to these shuffled measurements - the mean estimate computed from these surrogate realizations is the desired estimate. We used synthetic observations and real meteorological time series to verify the performance of our method; we found that the combination of r-LOS and bootstrapping resulted in estimates more accurate than when either approach was implemented separately.