A procedure for efficient estimation of the trimmed mean of a random variable conditional on a set of covariates is proposed. For concreteness, the focus is on a financial application where the trimmed mean of interest corresponds to the conditional expected shortfall, which is known to be a coherent risk measure. The proposed class of estimators is based on representing the estimator as an integral of the conditional quantile function. Relative to the simple analog estimator that weights all conditional quantiles equally, asymptotic efficiency gains may be attained by giving different weights to the different conditional quantiles while penalizing excessive departures from uniform weighting. The approach presented here allows for either parametric or nonparametric modeling of the conditional quantiles and the weights, but is essentially nonparametric in spirit. The asymptotic properties of the proposed class of estimators are established. Their finite sample properties are illustrated through a set of Monte Carlo experiments and an empirical application

SUMMARYUnlike the value at risk, the expected shortfall is a coherent measure of risk. In this paper, we discuss estimation of the expected shortfall of a random variable Y t with special reference to the case when auxiliary information is available in the form of a set of predictors X t . We consider three classes of estimators of the conditional expected shortfall of Y t given X t : a class of fully non-parametric estimators and two classes of analog estimators based, respectively, on the empirical conditional quantile function and the empirical conditional distribution function. We study their sampling properties by means of a set of Monte Carlo experiments and analyze their performance in an empirical application to financial data.

SUMMARYUnlike the value at risk, the expected shortfall is a coherent measure of risk. In this paper, we discuss estimation of the expected shortfall of a random variable Y t with special reference to the case when auxiliary information is available in the form of a set of predictors X t . We consider three classes of estimators of the conditional expected shortfall of Y t given X t : a class of fully non-parametric estimators and two classes of analog estimators based, respectively, on the empirical conditional quantile function and the empirical conditional distribution function. We study their sampling properties by means of a set of Monte Carlo experiments and analyze their performance in an empirical application to financial data.