Title: A Nonparametric Method for Producing Isolines of Bivariate Exceedance Probabilities,
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.