A Nonparametric Method for Producing Isolines of Bivariate Exceedance Probabilities

TitleA Nonparametric Method for Producing Isolines of Bivariate Exceedance Probabilities
Publication TypeJournal Article
Year of Publication2019
JournalExtremes
Date Published05/2019
Abstract / Summary

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. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities and may even lie beyond the range of the data; such cases would be problematic for standard nonparametric methods. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from hidden regular variation in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing the isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.

URLhttp://dx.doi.org/10.1007/s10687-019-00348-0
DOI10.1007/s10687-019-00348-0
Journal: Extremes
Year of Publication: 2019
Date Published: 05/2019

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. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities and may even lie beyond the range of the data; such cases would be problematic for standard nonparametric methods. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from hidden regular variation in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing the isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.

DOI: 10.1007/s10687-019-00348-0
Citation:
Cooley, D, E Thibaud, F Castillo, and M Wehner.  2019.  "A Nonparametric Method for Producing Isolines of Bivariate Exceedance Probabilities."  Extremes.  https://doi.org/10.1007/s10687-019-00348-0.