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Reduced-bias estimation of the residual dependence index with unspecified marginals

Lookup NU author(s): Dr David WalshawORCiD

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Abstract

© 2026, Institute of Mathematical Statistics. All rights reserved. This paper addresses important weaknesses in current methodology for the estimation of multivariate extreme event distributions. The estimation of the residual dependence index e (0, 1] is notoriously problematic. This motivates us to introduce a flexible class of gradient estimators for this parameter, designed to ameliorate the usual problems of threshold selection while furnishing a unifying approach to the usual marginal transforms. The efficacy of this semi-parametric gradient estimation of originates from a hitherto neglected exponentially decaying term in the hidden regular variation characterisation. Numerical simulations aimed at assessing the performance for finite samples over a range of familiar copulas indicate an improved performance relatively to the existing estimators, notably the Hill’s. Paired with a reduced-bias procedure that we also construct, the gradient estimation offers much desired statistical guarantees as it further pinpoints the optimal number of intermediate data points to enter the estimation (in terms of minimising asymptotic mean squared error) in an automatic and demonstrable way. Our leading application illustrates how asymptotic independence can be discerned from monsoon-related rainfall occurrences at different locations in Ghana. The considerations involved in extending this framework to inference on the extreme value index drawing on max-domains of attraction are briefly discussed. MSC2020 subject classifications: Primary 60F17, 62G32; secondary 62A99, 62P12.

Publication metadata

Author(s): Israelsson J, Black E, Neves C, Walshaw D

Publication type: Article

Publication status: Published

Journal: Electronic Journal of Statistics

Year: 2026

Volume: 20

Issue: 2

Pages: 2853-2891

Online publication date: 07/07/2026

Acceptance date: 02/04/2018

Date deposited: 10/08/2026

ISSN (electronic): 1935-7524

Publisher: Institute of Mathematical Statistics

URL: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-20/issue-2/Reduced-bias-estimation-of-the-residual-dependence-index-with-unspecified/10.1214/26-EJS2548.full

DOI: 10.1214/26-EJS2548

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