Asymptotically efficient estimation of the conditional expected shortfall

Samantha Leorato, Franco Peracchi and Andrei V. Tanase

Computational Statistics & Data Analysis, 2012, vol. 56, issue 4, 768-784

Abstract: 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 application11The Stata and Matlab codes used in the simulations and in the empirical analysis are available as annexes to the electronic version of the paper..

Keywords: Expected shortfall; Quantile regression; Asymptotic efficiency (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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Related works:
Working Paper: Asymptotically Efficient Estimation of the Conditional Expected Shortfall (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:4:p:768-784

DOI: 10.1016/j.csda.2011.02.020

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