统计与数据科学系系列学术报告之四百五十一期

时间：2024年9月24日（星期二）10:00-11:00

地点：史带楼303室

主持人：复旦大学管理学院统计与数据科学系黎德元教授

报告人：Prof. Chen Zhou Erasmus University Rotterdam (荷兰)

题目：Tail Copula Estimation for Heteroscedastic Extremes

摘要： Consider independent multivariate random vectors which follow the same copula, but where each marginal distribution is allowed to be non-stationary. This non-stationarity is for each marginal governed by a scedasis function that is the same for all marginals. We establish the asymptotic normality of the usual rank-based estimator of the stable tail dependence function, or, when specialized to bivariate random vectors, the corresponding estimator of the tail copula. Remarkably, the heteroscedastic marginals do not affect the limiting process. Next, under a bivariate setup, we develop nonparametric tests for testing whether the scedasis functions are the same for both marginals. Detailed simulations show the good performance of the estimator for the tail dependence coefficient as well as that of the new tests. In particular, novel asymptotic confidence intervals for the tail dependence coefficient are presented and their good finite-sample behavior is shown. Finally, an application to the S&P500 and Dow Jones indices reveals that their scedasis functions are about equal and that they exhibit strong tail dependence. This is a joint work with John Einmahl (Tilburg University).

个人简介：Prof. Chen Zhou is Professor of Mathematical Statistics and Risk Management at the Econometrics Institute, Erasmus University Rotterdam. His research focuses on extreme value statistics and its applications in quantitative risk management, financial stability and financial regulation. His statistical work has been published in statistical journals such as Annals of Statistics, Journal of Royal Statistical Society (Series B) and Journal of American Statistical Association. His applied work has been published in economic and finance journals such as Journal of Finance, Journal of Financial and Quantitative Analysis, and Journal of Economic Theory. Chen is also the area editor of Extremes in Economics, Finance and Insurance.