Expected shortfall or Conditional Value-at-Risk, measuring the average outcome (e.g., portfolio loss) above a given quantile of its probability distribution, is a common financial risk measure. The same measure can be used to characterize treatment effects in the tail of an outcome distribution, with applications ranging from policy evaluation in economics and public health to biomedical investigations. As we look deeper into data heterogeneity, the evaluation of covariate-adjusted expected shortfalls becomes more relevant but also more challenging. We discuss the alternative notion of super-quantile from the literature, and use it to motivate a new optimization-based approach to expected shortfall regression.

Xuming He is H.C. Carver Professor of Statistics, University of Michigan. Currently He is President-Elect of the International Statistical Institute (ISI). He served as Program Director of Statistics at the National Science Foundation and Co-Editor of the Journal of the American Statistical Association (JASA). Xuming He is Fellow of the American Association for the Advancement of Science (AAAS), the American Statistical Association (ASA), and the Institute of Mathematical Statistics (IMS). His recent honors and awards also include the Distinguished Faculty Achievement Award from the University of Michigan, the Founders Award (2021) from the American Statistical Association and the Carver Medal (2022) from the Institute of Mathematical Statistics. His research interests include theory and methodology in robust statistics, quantile regression, Bayesian computation, and post-selection inference. His interdisciplinary research aims to promote the better use of statistics in biosciences, climate studies, concussion research, and social-economic studies