Multi-Quantile Estimators for the parameters of Generalized Extreme Value distribution

TL;DR

This paper proposes Multi-Quantile estimators for GEV distribution parameters that are robust, asymptotically normal, and efficient across all parameter values, improving upon classical methods.

Contribution

Introduction of Multi-Quantile estimators for GEV parameters that are flexible, asymptotically normal, and closely approach the Cramér-Rao bound, unlike traditional estimators.

Findings

Estimators are asymptotically normal and consistent for all GEV parameters.

Variance decreases with more quantiles, nearing the Cramér-Rao bound.

Applicable within the Block Maxima method context.

Abstract

We introduce and study Multi-Quantile estimators for the parameters $( \xi, \sigma, \mu)$ of Generalized Extreme Value (GEV) distributions to provide a robust approach to extreme value modeling. Unlike classical estimators, such as the Maximum Likelihood Estimation (MLE) estimator and the Probability Weighted Moments (PWM) estimator, which impose strict constraints on the shape parameter $\xi$, our estimators are always asymptotically normal and consistent across all values of the GEV parameters. The asymptotic variances of our estimators decrease with the number of quantiles increasing and can approach the Cram\'er-Rao lower bound very closely whenever it exists. Our Multi-Quantile Estimators thus offer a more flexible and efficient alternative for practical applications. We also discuss how they can be implemented in the context of Block Maxima method.