Modeling Precipitation Extremes using Log-Histospline

One of the commonly used approaches to modeling univariate extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a (sufficiently high/low) threshold as a generalized Pareto distribution (GPD). To apply this method, a threshold has to be chosen and the estimates might be sensitive to the chosen threshold. Here we propose an alternative, the "Log-Histospline", to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. Log-Histospline applies smoothing spline on a finely binned histogram of the log transformed data to estimate its log density. By construction, we are able to preserve the polynomial tail behavior, a feature commonly observed in daily rainfall data. The Log-Histospline can be extended to the spatial setting by treating the marginal (log) density at each location as spatially indexed functional data, and perform a dimension reduction and spatial smoothing. We illustrate the proposed method by analyzing precipitation data from both regional climate model output (North American Regional Climate Change and Assessment Program (NARCCAP)) and weather stations in China.