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Threshold selection is a critical issue for extreme value analysis withthreshold-based approaches. Under suitable conditions, exceedances over a highthreshold have been shown to follow the generalized Pareto distribution (GPD)asymptotically. In practice, however, the threshold must be chosen. If thechosen threshold is too low, the GPD approximation may not hold and bias canoccur. If the threshold is chosen too high, reduced sample size increases thevariance of parameter estimates. To process batch analyses, commonly usedselection methods such as graphical diagnosis are subjective and cannot beautomated, while computational methods may not be feasible. We propose to testa set of thresholds through the goodness-of-fit of the GPD for the exceedances,and select the lowest one, above which the data provides adequate fit to theGPD. Previous attempts in this setting are not valid due to the special featurethat the multiple tests are done in an ordered fashion. We apply two recentlyavailable stopping rules that control the false discovery rate or familywiseerror rate to ordered goodness-of-fit tests to automate threshold selection.Various model specification tests such as the Cramer-von Mises,Anderson-Darling, Moran's, and a score test are investigated. The performanceof the method is assessed in a large scale simulation study that mimicspractical return level estimation. This procedure was repeated at hundreds ofsites in the western US to generate return level maps of extreme precipitation.

Automated Threshold Selection for Extreme Value Analysis via Goodness-of-Fit Tests with Application to Batched Return Level Mapping