摘要：We consider extreme value analysis in a semi-supervised setting, where we observe, next to the n data on the target variable, n+m data on one or more covariates. This is called the semi-supervised model with n labeled and m unlabeled data. By exploiting the tail dependence between the target variable and the covariates, we derive an estimator for the extreme value index of the target variable in this setting and establish its asymptotic behavior. Our estimator substantially improves the univariate estimator, based on only the n target variable data, in terms of asymptotic variance whereas the asymptotic bias remains unchanged. We present a simulation study in which the asymptotic results are confirmed and also an extreme quantile estimator is derived and its improved performance is shown. Finally the estimation method is applied to rainfall data in France.

报告人介绍：Prof. Chen Zhou is Professor of Mathematical Statistics and Risk Management at Erasmus University Rotterdam. He is also Senior Economist at De Nederlandsche Bank (Dutch Central Bank). His research focuses on extreme value statistics and quantitative risk management. His statistical work appears in Annals of Statistics, Journal of the Royal Statistical Society (Series B), Journal of American Statistical Association, Biometrika, among others. In addition, his research spans to the field of finance and economics, and has been published in leading journals including Journal of Financial and Quantitative Analysis and Journal of Economic Theory. Chen Zhou serves as the Area Editor of Economics, Finance and Insurance at the journal Extremes. He received his PhD (2008) from Erasmus University Rotterdam, after completing his Bachelor (2001) and Master (2003) degrees at Peking University.