Semi-parametric estimation of multivariate extreme expectiles

This paper focuses on semi-parametric estimation of multivariate expectiles for extreme levels risk. Multivariate and their extremes have been the focus plentiful research in recent years. In particular, it has noted that due to difficulty estimating these values elevated risk, an alternative formulation underlying optimization problem would be necessary. However, such a scenario, estimators only provided limiting cases tail dependence: independence comonotonicity. this paper, we extend (MEEs) by providing consistent scheme random vectors with any arbitrary dependence structure. Specifically, show if upper function, index, ratio can consistently estimated, then one able accurately estimate MEEs. The finite-sample performance methodology is illustrated using both simulated real data.