Expected Shortfall Regression for Censored Data

Abstract

Expected shortfall (ES), which conveys information regarding potential exceedances beyond the value-at-risk (VaR), is an important measure to characterize the properties of the tails of distribution. In this article, we study two two-step estimation procedures for ES regression with censored responses. Considering the potential dependence between the censoring variable and the covariates, two locally weighted estimation algorithms are proposed based on local Kaplan–Meier estimation and the joint elicitability of VaR and ES. The potential applications of this work are manifold, especially survival analysis, pharmacodynamic analysis, and sociological investigations. The resulting estimators are shown to be consistent. Extensive simulations demonstrate that the proposed method performs quite well in finite samples, with regard to estimation bias and mean squared errors. Last, the analysis of a real dataset illustrates the usefulness of our developed methodologies.

The online version contains supplementary material available at https://doi.org/10.1007/s40304-023-00357-3.

Keywords

Random censoring / Expected shortfall regression / Kaplan–Meier / Value-at-risk / 62N01 / 62G08

Funding

National Natural Science Foundation of China(Grant No. 71973133)

Anhui Provincial Natural Science Foundation(Grant No. 2208085J41)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature