New Exploratory Tools for Extremal Dependence: chi Networks and Annual Extremal Networks

摘要

Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work, we propose the chi network and the annual extremal network for exploring the extremal dependence structure of environmental processes. A chi network is constructed by connecting pairs whose estimated upper tail dependence coefficient, (chi) over cap, exceeds a prescribed threshold. We develop an initial chi network estimator, and we use a spatial block bootstrap to assess both the bias and variance of our estimator. We then develop a method to correct the bias of the initial estimator by incorporating the spatial structure in chi. In addition to the chi network, which assesses spatial extremal dependence over an extended period of time, we further introduce an annual extremal network to explore the year-to-year temporal variation of extremal connections. We illustrate the chi and the annual extremal networks by analyzing the hurricane season maximum precipitation at the US Gulf Coast and surrounding area. Analysis suggests there exists long distance extremal dependence for precipitation extremes in the study region and the strength of the extremal dependence may depend on some regional scale meteorological conditions, for example, sea surface temperature.