Asymptotically Efficient Estimation of the Conditional Expected Shortfall
AbstractThis paper proposes a procedure for efficient estimation of the trimmed mean of a random variable conditional on a set of covariates. For concreteness, the paper focuses 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 estimand 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 paper establishes the asymptotic properties of the proposed class of estimators. Their finite sample properties are illustrated through a set of Monte Carlo experiments and an empirical application.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Einaudi Institute for Economics and Finance (EIEF) in its series EIEF Working Papers Series with number 1013.
Length: 28 pages
Date of creation: 2010
Date of revision: Dec 2010
Other versions of this item:
- Leorato, Samantha & Peracchi, Franco & Tanase, Andrei V., 2012. "Asymptotically efficient estimation of the conditional expected shortfall," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(4), pages 768-784.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koenker,Roger, 2005.
Cambridge Books, Cambridge University Press,
Cambridge University Press, number 9780521845731.
- Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 15(4), pages 143-156, Fall.
- Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521608275.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Moller, Jan Kloppenborg & Nielsen, Henrik Aalborg & Madsen, Henrik, 2008. "Time-adaptive quantile regression," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(3), pages 1292-1303, January.
- Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 38(4), pages 433-447, February.
- Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," CEIS Research Paper, Tor Vergata University, CEIS 122, Tor Vergata University, CEIS, revised 14 Jul 2008.
- Giuseppe De Luca, 2008. "SNP and SML estimation of univariate and bivariate binary-choice models," Stata Journal, StataCorp LP, StataCorp LP, vol. 8(2), pages 190-220, June.
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, Elsevier, vol. 7(3-4), pages 271-300, November.
- Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 497-528, May.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007.
"Quantile And Probability Curves Without Crossing,"
Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics
WP2007-011, Boston University - Department of Economics.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006.
"Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure,"
Econometrica, Econometric Society,
Econometric Society, vol. 74(2), pages 539-563, 03.
- Joshua Angrist & Victor Chernozhukov & Ivan Fernandez-Val, 2004. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," NBER Working Papers 10428, National Bureau of Economic Research, Inc.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
- Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(7), pages 1353-1381, April.
- Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 82(2), pages 235-287, February.
- Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 169-192, February.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
- Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6631, London School of Economics and Political Science, LSE Library.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
- Huixia Judy Wang & Xiao-Hua Zhou, 2010. "Estimation of the retransformed conditional mean in health care cost studies," Biometrika, Biometrika Trust, Biometrika Trust, vol. 97(1), pages 147-158.
- Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, Elsevier, vol. 147(1), pages 120-130, November.
- Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 52(3), pages 459-470, September.
- Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1505-1518, July.
- Chun, So Yeon & Shapiro, Alexander & Uryasev, Stan, 2011. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," MPRA Paper 30132, University Library of Munich, Germany.
- Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(1), pages 140-154.
- Marcelo Brutti Righi & Paulo Sergio Ceretta, 2013. "Pair Copula Construction based Expected Shortfall estimation," Economics Bulletin, AccessEcon, vol. 33(2), pages 1067-1072.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Facundo Piguillem).
If references are entirely missing, you can add them using this form.