Estimation of Expectile‐Based Marginal Expected Shortfall Under Asymptotic Independence

Abstract

The expectile‐based marginal expected shortfall (XMES) is an analogue of the quantile‐based marginal expected shortfall (QMES). We study the asymptotic behaviour of XMES when the underlying random variables are asymptotically independent. We consider two different methods for the estimation of XMES: one based on least asymmetrically weighted squares and the other making use of the QMES. We establish the asymptotic theories for both estimators. Additionally, we investigate the finite sample performance of our methods through a simulation study and present a concrete application to financial data.