Estimating Equations for Spatial Extremes with Applications to Detection and Attribution Analysis of Changes in Climate Extremes

In inference for max-stable processes in regional frequency analysis, it is found that, when the dependence model is misspecified, the pairwise likelihood method leads to biased estimator. Motivated by the fact that the primary interest in many studies is the inference about marginal generalized extreme value (GEV) parameters and that the spatial dependence is a nuisance, we propose a combined score equations (CSE) approach that does not need dependence assumptions beyond the univariate GEV distribution. The CSE method combines the score equations of GEV model at each site with an approximate correlation function of the scores to improve the estimation efficiency. Applied to fingerprinting of changes in climate extremes with a coordinate descent algorithm to estimate a large number of parameters, the CSE method provides a close analog to the optimal fingerprinting in detection and attribution of changes in climate extremes. The CSE approach with working independence reduces to the independence likelihood method, but the estimation is much faster. This approach is applied on four annual extreme temperature indices during 1951--2010 over 17 subcontinents. In the single-signal analyses, anthropogenic and natural influence can be detected in all four indices separately. We also studied the two-signal analyses that both anthropogenic signal and natural signal are present in the model simultaneously, which has not been reported before under the extreme value framework due to methodological limitations. The anthropogenic signal is separable from natural signal in a few regions of the four indices