# Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials

arXiv: https://arxiv.org/abs/1405.5228 · HTML: https://mlsanity.com/paper/1405.5228/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2014.

## Built on by (most cited first, 3 of 3)

- [Modeling Extremes with d-max-decreasing Neural Networks](https://mlsanity.com/paper/2102.09042/) (2021)
- [High-dimensional variable clustering based on maxima of a weakly dependent random process](https://mlsanity.com/paper/2302.00934/) (2023)
- [Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions](https://mlsanity.com/paper/2408.00131/) (2024)

## Abstract (arXiv)

Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated by analyzing clusters consisting of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011.