On estimating conditional quantiles and distribution functions
Computational Statistics & Data Analysis - Nonlinear methods and data mining
Time-adaptive quantile regression
Computational Statistics & Data Analysis
On estimating the conditional expected shortfall
Applied Stochastic Models in Business and Industry - Special issue on statistical methods in performance analysis
Editorial for the special issue on quantile regression and semiparametric methods
Computational Statistics & Data Analysis
Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics
Operations Research
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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.