Where does the tail begin? An approach based on scoring rules
针对尾部指数估计对尾部观测数量k值敏感的问题，提出一种利用评分规则数据驱动选择k值的方法，确定尾部起始点，并在多元系统风险应用中展示其优势，通过模拟和美股VaR预测验证效果。
Learning about the tail shape of time series is important in, e.g., economics, finance, and risk management. However, it is well known that estimates of the tail index can be very sensitive to the choice of the number k of tail observations used for estimation. We propose a procedure that determines where the tail begins by choosing k in a data-driven fashion using scoring rules. So far, scoring rules have mainly been used to compare density forecasts. We also demonstrate how our proposal can be used in multivariate applications in the system risk literature. The advantages of our choice of k are illustrated in simulations and an empirical application to Value-at-Risk forecasts for five U.S. blue-chip stocks.