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

Israelsson, J. ORCID: https://orcid.org/0000-0001-6181-1702, Black, E. ORCID: https://orcid.org/0000-0003-1344-6186, Neves, C. ORCID: https://orcid.org/0000-0003-1201-5720 and Walshaw, D. (2026) Reduced-bias estimation of the residual dependence index with unspecified marginals. Electronic journal of statistics, 20 (2). pp. 2853-2891. ISSN 1935-7524 doi: 10.1214/26-EJS2548

Abstract/Summary

This paper addresses important weaknesses in current methodology for the estimation of multivariate extreme event distributions. The estimation of the residual dependence index η∈(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 η 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.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/131553
Identification Number/DOI	10.1214/26-EJS2548
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > NCAS Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Institute of Mathematical Statistics
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