There are some suggestions that extreme weather events are becoming more frequent due to global warming. From a statistical point of view, this raises the question of trend detection in the extremes of a series of observations. We build upon the heteroscedastic extremes framework by Einmahl et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78(1), 31–51, 2016) where the observations are assumed independent but not identically distributed and the variation in their tail distributions is modeled by the so-called skedasis function. While the original paper focuses on non parametric estimation of the skedasis function, we consider here parametric models and prove the consistency and asymptotic normality of the parameter estimators. A parametric test for trend detection in the case where the skedasis function is monotonic is introduced. A short simulation study shows that the parametric test can be more powerful than the non parametric Kolmogorov-Smirnov type test, even for misspecified models. The methodology is finally illustrated on a dataset of daily maximal temperatures in Fort Collins, Colorado, during the 20th century.

中文翻译：

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极端误差趋势检测

有一些建议表明，由于全球变暖，极端天气事件变得越来越频繁。从统计角度来看，这在一系列观察的极端情况下提出了趋势检测的问题。我们基于Einmahl等人的异方差极端框架。（JR统计会志序列B.统计。Methodol。78（1），31-51，2016），其中观察值被认为是独立的，但分布不相同，并且它们的尾巴分布的变化通过所谓的skedasis函数建模。虽然原始论文专注于skedasis函数的非参数估计，但我们在这里考虑参数模型并证明参数估计器的一致性和渐近正态性。介绍了在skedasis函数为单调的情况下用于趋势检测的参数测试。简短的仿真研究表明，即使对于指定不正确的模型，参数测试也可以比非参数Kolmogorov-Smirnov型测试更强大。最后，该方法在20世纪科罗拉多州柯林斯堡的每日最高温度数据集中得到了说明。