Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to ExtremeValue Data
Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to ExtremeValue Data
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DOI：
10.1214/ss/1009212755
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发表时间：
2000-05
影响因子：
5.7
通讯作者：
P. Hall;N. Tajvidi
中科院分区：
文献类型：
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作者：
P. Hall;N. Tajvidi
当前极值分析中的一个主要兴趣是时间趋势的研究。例如，“温室”效应的潜在影响可能会导致严重风暴逐渐变得格拉德频繁，或者最高温度随着时间的推移逐渐升高。评估这些可能性的一种方法是拟合数据，时间参数变化的参数模型，以及描述在任何给定时间点的数据的边缘分布的模型。然而，由于不同因素联合收割机以极端形式影响数据的复杂方式，在许多情况下可能难以制定结构趋势模型。此外，在没有经验证据证明其适用性的情况下拟合趋势模型是不可取的。在本文中，由数据集的风暴强度和最高温度的动机，我们提出了一种非参数方法来估计时间趋势时，拟合参数模型的极值从弱相关的时间序列。我们说明了通过应用程序的时间序列的边缘分布近似帕累托，广义帕累托，极值或高斯的方法。我们引入时变概率图来评估拟合优度，我们讨论了局部似然方法来拟合窗口内的边缘模型，并提出了时间交叉验证来选择窗口宽度。在位置和规模估计在一起的情况下，高斯分布具有特殊的功能，允许它发挥作为一个“名义”模型的边缘分布的普遍作用。
A topic of major current interest in extreme-value analysis is the investigation of temporal trends. For example, the potential influ- ence of "greenhouse" effects may result in severe storms becoming grad- ually more frequent, or in maximum temperatures gradually increasing, with time. One approach to evaluating these possibilities is to fit, to data, a parametric model for temporal parameter variation, as well as a model describing the marginal distribution of data at any given point in time. However, structural trend models can be difficult to formulate in many circumstances, owing to the complex way in which different factors combine to influence data in the form of extremes. Moreover, it is not advisable to fit trend models without empirical evidence of their suitability. In this paper, motivated by datasets on windstorm severity and maximum temperature, we suggest a nonparametric approach to estimating temporal trends when fitting parametric models to extreme values from a weakly dependent time series. We illustrate the method through applications to time series where the marginal distributions are approximately Pareto, generalized-Pareto, extreme-value or Gaussian. We introduce time-varying probability plots to assess goodness of fit, we discuss local-likelihood approaches to fitting the marginal model within a window and we propose temporal cross-validation for selecting window width. In cases where both location and scale are estimated together, the Gaussian distribution is shown to have special features that permit it to play a universal role as a "nominal" model for the marginal distribution.