用对数组织样条估计极端降水量
Estimating Precipitation Extremes using Log-Histospline
摘要：
建模极值的常用方法之一是峰值超过阈值（POT）方法。POT方法在足够高或足够低的阈值上对双方差进行建模，使得双方差近似具有广义帕累托分布（GPD）。这种方法需要选择一个可能影响估计数的阈值。在这里，我们提出了一种替代方法，对数组织样条（LHSpline），探索建模的尾部行为和剩余的密度在一个步骤中使用的全范围的数据。LHSpline将平滑样条模型应用于对数转换数据的精细分箱直方图，以估计其对数密度。通过构造，LHSpline估计被约束为具有多项式尾部行为，这是日常降雨观测中常见的特征。我们说明LHSpline方法通过分析在得克萨斯州休斯顿收集的降水数据。
英文摘要：
One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high or low so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing precipitation data collected in Houston, Texas.
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