Statistics – Methodology
Scientific paper
2012-04-02
Statistics
Methodology
Scientific paper
Max-stable processes have recently been used in modeling spatial extremes. Due to unavailable full likelihood, inferences have to rely on composite likelihood constructed from bivariate or trivariate marginal densities. Since max-stable processes specify the dependence of block maxima, the data used for inference are block maxima from all sites. The point process approach or the peaks over threshold approach for univariate extreme value analysis, which uses more data and is preferred by practitioners, does not adapt easily to the spatial setting. To use more data in spatial extremes modeling, we propose a composite likelihood approach that fuses block maxima data with daily records. The procedure separates the estimation of marginal parameters and dependence parameters in two steps. The first step estimates marginal parameters using an independent composite likelihood from the point process approach with daily records. Given the marginal parameter estimates, the second step estimates the dependence parameters by a pairwise likelihood with block maxima. Based on the theory of inference functions, the asymptotic consistency and asymptotic normality can be established, and the limiting covariance matrix is estimated with a sandwich variance estimator. In a simulation study, the two-step estimator was found to be more efficient, and in some scenarios much more, than the existing composite likelihood approach based on block maxima data only. The practical utility is illustrated through the precipitation data at 20 sites in California over 55 years, and the two-step estimator gives much tighter confidence regions for risk measures of jointly defined events.
Shang Hongwei
Yan Jun
Zhang Xuebin
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