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首页> 外文期刊>Electronic Journal of Statistics >The spectrogram: A threshold-based inferential tool for extremes of stochastic processes
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The spectrogram: A threshold-based inferential tool for extremes of stochastic processes

机译：频谱图：基于阈值的推理工具，用于极端随机过程

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We extend the statistical toolbox for inferring the extreme value behavior of stochastic processes by defining the spectrogram. It is based on a pseudo-polar representation of bivariate data and represents a collection of spectral measures that characterize the bivariate extremal dependence structure in terms of a univariate distribution. Based on threshold exceedances in the original event data, estimation of the spectrogram is flexible and efficient. The virtues of the spectrogram for exploratory studies and for parametric inference are highlighted. We propose a variance reduction technique that can be applied to the estimation of summary statistics like the extremogram. Parametric inference based on distance measures between the empirical and the model spectrogram, as for instance pairwise likelihoods or least squares distances, is developed. Simulated data illustrate gains in parametric estimation efficiency compared to a standard estimation approach. An application to precipitation data collected in the Cévennes region in France shows the practical utility of the introduced notions.
机译：我们通过定义频谱图来扩展统计工具箱，以推断随机过程的极值行为。它基于双变量数据的伪极性表示，并表示光谱度量的集合，这些光谱度量以单变量分布为特征来表征双变量极值依赖性结构。基于原始事件数据中的阈值超出，频谱图的估计是灵活而高效的。强调了频谱图在探索性研究和参数推断中的优点。我们提出了一种方差减少技术，可以将其应用于汇总统计信息（如极值图）的估计。建立了基于经验和模型频谱图之间的距离度量的参数推断，例如成对似然或最小二乘方距离。仿真数据说明了与标准估算方法相比，参数估算效率的提高。对法国塞文山脉地区收集的降水数据的应用表明，引入的概念具有实际用途。

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