A Nonparametric Method for Producing Isolines of Bivariate Exceedance Probabilities

TL;DR

This paper introduces a nonparametric approach for constructing isolines of joint exceedance probabilities in bivariate data, useful for extreme value analysis and applicable beyond data ranges.

Contribution

It extends existing methods by enabling isoline drawing for very low probabilities, including cases of asymptotic independence, with new smoothing and diagnostic techniques.

Findings

Effective in estimating extreme joint exceedance regions

Handles asymptotic independence with smoothing transition

Provides uncertainty assessment via bootstrap

Abstract

We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. This framework enables drawing isolines corresponding to very low exceedance probabilities and these lines may lie beyond the range of the data. The method we utilize for characterizing dependence in the tail is largely nonparametric. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from asymptotic independence in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.