{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T12:18:24Z","timestamp":1791893904745,"version":"4.3.4"},"reference-count":58,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T00:00:00Z","timestamp":1686787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1914496"],"award-info":[{"award-number":["DMS-1914496"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1951980"],"award-info":[{"award-number":["DMS-1951980"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-2113346"],"award-info":[{"award-number":["DMS-2113346"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSF CAREER","award":["DMS-2238428"],"award-info":[{"award-number":["DMS-2238428"]}]},{"name":"NSF CAREER","award":["DMS-2113409"],"award-info":[{"award-number":["DMS-2113409"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Expected shortfall (ES), also known as superquantile or conditional value-at-risk, is an important measure in risk analysis and stochastic optimisation and has applications beyond these fields. In finance, it refers to the conditional expected return of an asset given that the return is below some quantile of its distribution. In this paper, we consider a joint regression framework recently proposed to model the quantile and ES of a response variable simultaneously, given a set of covariates. The current state-of-the-art approach to this problem involves minimising a non-differentiable and non-convex joint loss function, which poses numerical challenges and limits its applicability to large-scale data. Motivated by the idea of using Neyman-orthogonal scores to reduce sensitivity to nuisance parameters, we propose a statistically robust and computationally efficient two-step procedure for fitting joint quantile and ES regression models that can handle highly skewed and heavy-tailed data. We establish explicit non-asymptotic bounds on estimation and Gaussian approximation errors that lay the foundation for statistical inference, even with increasing covariate dimensions. Finally, through numerical experiments and two data applications, we demonstrate that our approach well balances robustness, statistical, and numerical efficiencies for expected shortfall regression.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad063","type":"journal-article","created":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T03:42:16Z","timestamp":1686800536000},"page":"1223-1246","source":"Crossref","is-referenced-by-count":16,"title":["Robust estimation and inference for expected shortfall regression with many regressors"],"prefix":"10.1093","volume":"85","author":[{"given":"Xuming","family":"He","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Washington University in St. Louis , St. Louis, MO , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kean Ming","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Michigan , Ann Arbor, MI , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2761-485X","authenticated-orcid":false,"given":"Wen-Xin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Information and Decision Sciences, University of Illinois at Chicago , Chicago, IL , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"issue":"1","key":"2024061500003913800_qkad063-B1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/1468-0262.00270","article-title":"Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings","volume":"70","author":"Abadie","year":"2002","journal-title":"Econometrica"},{"issue":"11","key":"2024061500003913800_qkad063-B2","first-page":"76","article-title":"Back-testing expected shortfall","volume":"27","author":"Acerbi","year":"2014","journal-title":"Risk"},{"issue":"7","key":"2024061500003913800_qkad063-B3","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1016\/S0378-4266(02)00283-2","article-title":"On the coherence of expected shortfall","volume":"26","author":"Acerbi","year":"2002","journal-title":"Journal of Banking & Finance"},{"issue":"2","key":"2024061500003913800_qkad063-B4","doi-asserted-by":"crossref","first-page":"307","DOI":"10.2307\/2938259","article-title":"Asymptotic normality of series estimators for nonparametric and semiparametric regression models","volume":"59","author":"Andrews","year":"1991","journal-title":"Econometrica"},{"key":"2024061500003913800_qkad063-B5","article-title":"Efficiently weighted estimation of tail and interquantile expectations","author":"Barendse","year":"2020","journal-title":"Preprint"},{"issue":"1","key":"2024061500003913800_qkad063-B6","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","article-title":"Two-point step size gradient methods","volume":"8","author":"Barzilai","year":"1988","journal-title":"IMA Journal of Numerical Analysis"},{"key":"2024061500003913800_qkad063-B7","author":"Basel Committee.","year":"2016"},{"key":"2024061500003913800_qkad063-B8","author":"Basel Committee.","year":"2019"},{"issue":"4","key":"2024061500003913800_qkad063-B9","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1093\/jjfinec\/nbh023","article-title":"Pessimistic portfolio allocation and Choquet expected utility","volume":"2","author":"Bassett","year":"2004","journal-title":"Journal of Financial Econometrics"},{"issue":"1","key":"2024061500003913800_qkad063-B10","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.jeconom.2019.04.003","article-title":"Conditional quantile processes based on series or many regressors","volume":"213","author":"Belloni","year":"2019","journal-title":"Journal of Econometrics"},{"issue":"11","key":"2024061500003913800_qkad063-B11","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1287\/mnsc.32.11.1445","article-title":"Expected utility, penalty functions, and duality in stochastic nonlinear programming","volume":"32","author":"Ben-Tal","year":"1986","journal-title":"Management Science"},{"issue":"3","key":"2024061500003913800_qkad063-B12","doi-asserted-by":"crossref","first-page":"549","DOI":"10.2307\/146183","article-title":"The benefits and costs of JTPA Title II-A programs: Key findings from the national job training partnership act study","volume":"32","author":"Bloom","year":"1997","journal-title":"The Journal of Human Resources"},{"issue":"1","key":"2024061500003913800_qkad063-B13","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jeconom.2008.09.005","article-title":"Nonparametric estimation of conditional VaR and expected shortfall","volume":"147","author":"Cai","year":"2008","journal-title":"Journal of Econometrics"},{"issue":"19","key":"2024061500003913800_qkad063-B14","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1056\/NEJMra1401038","article-title":"Iron-deficiency anemia","volume":"372","author":"Camaschella","year":"2015","journal-title":"New England Journal of Medicine"},{"issue":"4","key":"2024061500003913800_qkad063-B15","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1214\/11-AIHP454","article-title":"Challenging the empirical mean and empirical variance: A deviation study","volume":"48","author":"Catoni","year":"2012","journal-title":"Annales de l\u2019Institut Henri Poincar\u00e9 Probabilit\u00e9s et Statistiques"},{"key":"2024061500003913800_qkad063-B16","doi-asserted-by":"crossref","first-page":"5549","DOI":"10.1016\/S1573-4412(07)06076-X","article-title":"Chapter 76 large sample sieve estimation of semi-nonparametric models","volume-title":"Handbook of Econometrics","author":"Chen","year":"2007"},{"issue":"4","key":"2024061500003913800_qkad063-B17","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1214\/aoms\/1177729330","article-title":"A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations","volume":"23","author":"Chernoff","year":"1952","journal-title":"The Annals of Mathematical Statistics"},{"issue":"1","key":"2024061500003913800_qkad063-B18","doi-asserted-by":"crossref","first-page":"C1","DOI":"10.1111\/ectj.12097","article-title":"Double\/debiased machine learning for treatment and structural parameters","volume":"21","author":"Chernozhukov","year":"2018","journal-title":"The Econometrics Journal"},{"issue":"1","key":"2024061500003913800_qkad063-B19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.jeconom.2007.06.005","article-title":"Instrumental variable quantile regression: A robust inference approach","volume":"142","author":"Chernozhukov","year":"2008","journal-title":"Journal of Econometrics"},{"issue":"2","key":"2024061500003913800_qkad063-B20","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/713665670","article-title":"Empirical properties of asset returns: Stylized facts and statistical issues","volume":"1","author":"Cont","year":"2001","journal-title":"Quantitative Finance"},{"key":"2024061500003913800_qkad063-B21","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-34471-3","volume-title":"Extreme value theory: An introduction","author":"de Haan","year":"2006"},{"issue":"1","key":"2024061500003913800_qkad063-B22","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1214\/19-EJS1560","article-title":"A joint quantile and expected shortfall regression framework","volume":"13","author":"Dimitriadis","year":"2019","journal-title":"Electronic Journal of Statistics"},{"issue":"4","key":"2024061500003913800_qkad063-B23","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1287\/mnsc.2015.2342","article-title":"Backtesting expected shortfall: Accounting for tail risk","volume":"63","author":"Du","year":"2017","journal-title":"Management Science"},{"issue":"410","key":"2024061500003913800_qkad063-B24","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1080\/01621459.1990.10476211","article-title":"Testing the goodness of fit of a linear model via nonparametric regression techniques","volume":"85","author":"Eubank","year":"1990","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2024061500003913800_qkad063-B25","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1111\/rssb.12166","article-title":"Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions","volume":"79","author":"Fan","year":"2017","journal-title":"Journal of the Royal Statistical Society Series B: Statistical Methodology"},{"issue":"1","key":"2024061500003913800_qkad063-B26","doi-asserted-by":"crossref","first-page":"181","DOI":"10.3982\/ECTA16901","article-title":"Deep neural networks for estimation and inference","volume":"89","author":"Farrell","year":"2021","journal-title":"Econometrica"},{"issue":"1","key":"2024061500003913800_qkad063-B27","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1080\/07350015.2019.1660177","article-title":"Smoothing quantile regressions","volume":"39","author":"Fernandes","year":"2021","journal-title":"Journal of Business & Economic Statistics"},{"issue":"4","key":"2024061500003913800_qkad063-B28","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1214\/16-AOS1439","article-title":"Higher order elicitability and Osband\u2019s principle","volume":"44","author":"Fissler","year":"2016","journal-title":"The Annals of Statistics"},{"issue":"494","key":"2024061500003913800_qkad063-B29","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1198\/jasa.2011.r10138","article-title":"Making and evaluating point forecasts","volume":"106","author":"Gneiting","year":"2011","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2024061500003913800_qkad063-B30","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1214\/aop\/1176990747","article-title":"The asymptotic joint distribution of self-normalized censored sums and sums of squares","volume":"18","author":"Hahn","year":"1990","journal-title":"The Annals of Probability"},{"issue":"4","key":"2024061500003913800_qkad063-B31","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1214\/10-AOAS347","article-title":"Detection of treatment effects by covariate-adjusted expected shortfall","volume":"4","author":"He","year":"2010","journal-title":"The Annals of Applied Statistics"},{"issue":"2","key":"2024061500003913800_qkad063-B32","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jeconom.2021.07.010","article-title":"Smoothed quantile regression with large-scale inference","volume":"232","author":"He","year":"2023","journal-title":"Journal of Econometrics"},{"issue":"5","key":"2024061500003913800_qkad063-B33","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1214\/aos\/1176342503","article-title":"Robust estimation: Asymptotics, conjectures and Monte Carlo","volume":"1","author":"Huber","year":"1973","journal-title":"The Annals of Statistics"},{"issue":"2","key":"2024061500003913800_qkad063-B34","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1093\/jjfinec\/nbs002","article-title":"Weighted Nadaraya\u2013Watson estimation of conditional expected shortfall","volume":"10","author":"Kato","year":"2012","journal-title":"Journal of Financial Econometrics"},{"issue":"1","key":"2024061500003913800_qkad063-B35","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/1913643","article-title":"Regression quantiles","volume":"46","author":"Koenker","year":"1978","journal-title":"Econometrica"},{"issue":"1-2","key":"2024061500003913800_qkad063-B36","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.cca.2007.02.012","article-title":"Age specific reference intervals for soluble transferrin receptor (sTfR)","volume":"380","author":"Kratovil","year":"2007","journal-title":"Clinica Chimica Acta"},{"issue":"4","key":"2024061500003913800_qkad063-B37","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1017\/S0266466612000692","article-title":"Estimation and inference about the expected shortfall for time series with infinite variance","volume":"29","author":"Linton","year":"2013","journal-title":"Econometric Theory"},{"issue":"1","key":"2024061500003913800_qkad063-B38","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1017\/S0266466616000517","article-title":"Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory","volume":"34","author":"Martins-Filho","year":"2018","journal-title":"Econometric Theory"},{"issue":"1","key":"2024061500003913800_qkad063-B39","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1093\/clinchem\/44.1.45","article-title":"Clinical utility of the soluble transferrin receptor and comparison with serum ferritin in several populations","volume":"44","author":"Mast","year":"1998","journal-title":"Clinical Chemistry"},{"key":"2024061500003913800_qkad063-B40","volume-title":"Quantitative risk management: Concepts, techniques and tools","author":"McNeil","year":"2015","edition":"2nd"},{"key":"2024061500003913800_qkad063-B41","volume-title":"Problem complexity and method efficiency in optimization","author":"Nemirovski","year":"1983"},{"issue":"1","key":"2024061500003913800_qkad063-B42","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0304-4076(97)00011-0","article-title":"Convergence rates and asymptotic normality for series estimators","volume":"79","author":"Newey","year":"1997","journal-title":"Journal of Econometrics"},{"issue":"1\/2","key":"2024061500003913800_qkad063-B43","first-page":"1","article-title":"C(\u03b1) tests and their use","volume":"41","author":"Neyman","year":"1979","journal-title":"Sankhya"},{"issue":"3","key":"2024061500003913800_qkad063-B44","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1093\/imaiai\/iaaa006","article-title":"Multiplier bootstrap for quantile regression: Non-asymptotic theory under random design","volume":"10","author":"Pan","year":"2021","journal-title":"Information and Inference: A Journal of the IMA"},{"issue":"2","key":"2024061500003913800_qkad063-B45","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.jeconom.2018.10.008","article-title":"Dynamic semiparametric models for expected shortfall (and value-at-risk)","volume":"211","author":"Patton","year":"2019","journal-title":"Journal of Econometrics"},{"key":"2024061500003913800_qkad063-B46","author":"Peng","year":"2022"},{"key":"2024061500003913800_qkad063-B47","first-page":"151","author":"Rockafellar","year":"2014"},{"issue":"1","key":"2024061500003913800_qkad063-B48","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.ejor.2013.10.046","article-title":"Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk","volume":"234","author":"Rockafellar","year":"2014","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"2024061500003913800_qkad063-B49","doi-asserted-by":"crossref","first-page":"21","DOI":"10.21314\/JOR.2000.038","article-title":"Optimization of conditional value-at-risk","volume":"2","author":"Rockafellar","year":"2000","journal-title":"The Journal of Risk"},{"issue":"7","key":"2024061500003913800_qkad063-B50","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1016\/S0378-4266(02)00271-6","article-title":"Conditional value-at-risk for general loss distributions","volume":"26","author":"Rockafellar","year":"2002","journal-title":"Journal of Banking & Finance"},{"issue":"23","key":"2024061500003913800_qkad063-B51","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1056\/NEJM199312023292303","article-title":"Evaluation of the gastrointestinal tract in patients with iron-deficiency anemia","volume":"329","author":"Rockey","year":"1993","journal-title":"New England Journal of Medicine"},{"issue":"1","key":"2024061500003913800_qkad063-B52","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1111\/j.0960-1627.2004.00184.x","article-title":"Nonparametric estimation and sensitivity analysis of expected shortfall","volume":"14","author":"Scaillet","year":"2004","journal-title":"Mathematical Finance"},{"issue":"4","key":"2024061500003913800_qkad063-B53","first-page":"1875","article-title":"Nonparametric regression using deep neural networks with ReLU activation function","volume":"48","author":"Schmidt-Hieber","year":"2020","journal-title":"The Annals of Statistics"},{"key":"2024061500003913800_qkad063-B54","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611973433","volume-title":"Lectures on stochastic programming: Modeling and theory","author":"Shapiro","year":"2014","edition":"2nd"},{"key":"2024061500003913800_qkad063-B55","author":"Shen","year":"2021"},{"issue":"500","key":"2024061500003913800_qkad063-B56","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1080\/01621459.2012.716382","article-title":"Estimation of high conditional quantiles for heavy-tailed distributions","volume":"107","author":"Wang","year":"2012","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"2024061500003913800_qkad063-B57","first-page":"2153","article-title":"A new principle for tuning-free Huber regression","volume":"31","author":"Wang","year":"2021","journal-title":"Statistica Sinica"},{"issue":"5","key":"2024061500003913800_qkad063-B58","doi-asserted-by":"crossref","first-page":"1904","DOI":"10.1214\/17-AOS1606","article-title":"A new perspective on robust M-estimation: Finite sample theory and applications to dependence-adjusted multiple testing","volume":"46","author":"Zhou","year":"2018","journal-title":"The Annals of Statistics"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/4\/1223\/51801392\/qkad063.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/4\/1223\/51801392\/qkad063.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T00:04:02Z","timestamp":1718409842000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/4\/1223\/7198207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,15]]},"references-count":58,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,6,15]]},"published-print":{"date-parts":[[2023,9,29]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkad063","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,9]]},"published":{"date-parts":[[2023,6,15]]}}}