Empirical Bayes estimation for the conditional extreme value model

A new estimation strategy for estimating the parameters of the Heffernan and Tawn conditional extreme value model is proposed. The technique makes use of empirical Bayes estimation for the conditional likelihood that otherwise does not have a simple closed-form expression. The approach is tested on simulations from different types of extreme dependence (and independence) structures, as well as for two real data cases consisting of precipitation analysis conditional on extreme temperature in Boulder, Colorado, and Los Angeles, California, USA. The strategy generally has good coverage when informative priors are used for one of the parameters, except for the independence case where the coverage is low until the sample size reaches about 50. Results for the precipitation and temperature data are found to be consistent with the semi-non-parametric strategy. The presented model can be potentially applied in a wide variety of science fields, especially in earth, environment and climate sciences.