{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T04:13:33Z","timestamp":1777868013512,"version":"3.51.4"},"reference-count":80,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["OR Spectrum"],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Shrinkage estimators reduce estimation risk in multivariate statistics such as mean and standard deviation. They have not been used before in data envelopment analysis (DEA). By considering models of investment fund returns, we show that estimation risk can cause the range of estimates of inputs and outputs in a DEA model to be overestimated so that shrinkage estimators should improve them. We show how to use shrinkage estimators for mean and standard deviation in DEA and develop a shrinkage estimator for expected shortfall. We further show how to adapt these estimators for diversification-consistent models. We illustrate DEA with shrinkage estimation on returns for hedge funds and find that using shrinkage estimators to improve the estimates of efficiencies tends to increase efficiency estimates without substantially changing their rank order.<\/jats:p>","DOI":"10.1007\/s00291-025-00828-9","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T02:14:48Z","timestamp":1753150488000},"page":"117-142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data envelopment analysis with shrinkage estimators"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5849-7772","authenticated-orcid":false,"given":"John D.","family":"Lamb","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5696-2311","authenticated-orcid":false,"given":"Kai-Hong","family":"Tee","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"828_CR1","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1080\/14697680701461590","volume":"7","author":"C Acerbi","year":"2007","unstructured":"Acerbi C (2007) Coherent measures of risk in everyday market practice. Quant Financ 7:359\u2013364. https:\/\/doi.org\/10.1080\/14697680701461590","journal-title":"Quant Financ"},{"issue":"31","key":"828_CR2","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1111\/1468-0300.00091","volume":"7","author":"C Acerbi","year":"2002","unstructured":"Acerbi C, Tasche D (2002) Expected shortfall: a natural coherent alternative to value at risk. Econ Notes 7(31):379\u2013388. https:\/\/doi.org\/10.1111\/1468-0300.00091","journal-title":"Econ Notes"},{"issue":"102","key":"828_CR3","doi-asserted-by":"publisher","first-page":"102338","DOI":"10.1016\/j.omega.2020.102338","volume":"7","author":"L Adam","year":"2021","unstructured":"Adam L, Branda M (2021) Risk-aversion in data envelopment analysis models with diversification. Omega 7(102):102338. https:\/\/doi.org\/10.1016\/j.omega.2020.102338","journal-title":"Omega"},{"key":"828_CR4","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0304-4076(77)90052-5","volume":"6","author":"D Aigner","year":"1977","unstructured":"Aigner D, Lovell C, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econom 6:21\u201337. https:\/\/doi.org\/10.1016\/0304-4076(77)90052-5","journal-title":"J Econom"},{"key":"828_CR5","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1002\/mde","volume":"30","author":"GJ Alexander","year":"2009","unstructured":"Alexander GJ, Baptista AM, Shu Y (2009) Reducing estimation risk in optimal portfolio selection when short sales are allowed. Manag Decis Econ 30:281\u2013305. https:\/\/doi.org\/10.1002\/mde","journal-title":"Manag Decis Econ"},{"key":"828_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/s00291-024-00794-8","author":"A Amirteimoori","year":"2024","unstructured":"Amirteimoori A, Charles V, Mehdizadeh S (2024) Stochastic data envelopment analysis in the presence of undesirable outputs: an application to the power industry. OR Spectr. https:\/\/doi.org\/10.1007\/s00291-024-00794-8","journal-title":"OR Spectr"},{"issue":"311","key":"828_CR7","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1016\/J.EJOR.2023.05.005","volume":"12","author":"A Arabmaldar","year":"2023","unstructured":"Arabmaldar A, Sahoo BK, Ghiyasi M (2023) A generalized robust data envelopment analysis model based on directional distance function. Eur J Oper Res 12(311):617\u2013632. https:\/\/doi.org\/10.1016\/J.EJOR.2023.05.005","journal-title":"Eur J Oper Res"},{"key":"828_CR8","doi-asserted-by":"crossref","unstructured":"Arnold BC, Balakrishnan N, Nagaraja HN (2008) A first course in order statistics. SIAM","DOI":"10.1137\/1.9780898719062"},{"key":"828_CR9","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"1999","unstructured":"Artzner P, Delbaen F (1999) Coherent measures of risk. Math Financ 9:203\u2013228. https:\/\/doi.org\/10.1111\/1467-9965.00068","journal-title":"Math Financ"},{"key":"828_CR10","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1016\/j.ijepes.2015.06.002","volume":"73","author":"A Azadeh","year":"2015","unstructured":"Azadeh A, Haghighi SM, Zarrin M, Khaefi S (2015) Performance evaluation of Iranian electricity distribution units by using stochastic data envelopment analysis. Int J Electr Power Energy Syst 73:919\u2013931. https:\/\/doi.org\/10.1016\/j.ijepes.2015.06.002","journal-title":"Int J Electr Power Energy Syst"},{"key":"828_CR11","doi-asserted-by":"crossref","unstructured":"Basso A, Funari S (2016) DEA performance assessment of mutual funds. In: Zhu J (ed) Data envelopment analysis: a handbook of empirical studies and applications, vol 238. International Series in Operations Research and Management Science. Springer, New York LLC, pp 229\u2013287","DOI":"10.1007\/978-1-4899-7684-0_8"},{"key":"828_CR12","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.jmva.2018.07.004","volume":"170","author":"T Bodnar","year":"2019","unstructured":"Bodnar T, Okhrin O, Parolya N (2019) Optimal shrinkage estimator for high-dimensional mean vector. J Multivar Anal 170:63\u201379. https:\/\/doi.org\/10.1016\/j.jmva.2018.07.004","journal-title":"J Multivar Anal"},{"key":"828_CR13","doi-asserted-by":"crossref","unstructured":"Bogetoft P, Otto L (2011) Benchmarking with DEA. SFA and R. Springer, Berlin","DOI":"10.1007\/978-1-4419-7961-2"},{"key":"828_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/jjfinec\/nby022","volume":"18","author":"K Boudt","year":"2018","unstructured":"Boudt K, Cornilly D, Verdonck T (2018) A coskewness shrinkage approach for estimating the skewness of linear combinations of random variables. J Financ Economet 18:1\u201323. https:\/\/doi.org\/10.1093\/jjfinec\/nby022","journal-title":"J Financ Economet"},{"key":"828_CR15","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1016\/j.ejor.2012.11.007","volume":"226","author":"M Branda","year":"2013","unstructured":"Branda M (2013) Diversification-consistent data envelopment analysis with general deviation measures. Eur J Oper Res 226:626\u2013635. https:\/\/doi.org\/10.1016\/j.ejor.2012.11.007","journal-title":"Eur J Oper Res"},{"key":"828_CR16","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.omega.2014.11.004","volume":"52","author":"M Branda","year":"2015","unstructured":"Branda M (2015) Diversification-consistent data envelopment analysis based on directional-distance measures. Omega 52:65\u201376. https:\/\/doi.org\/10.1016\/j.omega.2014.11.004","journal-title":"Omega"},{"key":"828_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/B:JOTA.0000012730.36740.bb","volume":"120","author":"W Briec","year":"2004","unstructured":"Briec W, Kerstens K, Lesourd JB (2004) Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function 1. J Optim Theory Appl 120:1\u201327","journal-title":"J Optim Theory Appl"},{"issue":"53","key":"828_CR18","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1287\/MNSC.1060.0596","volume":"1","author":"W Briec","year":"2007","unstructured":"Briec W, Kerstens K, Jokung O (2007) Mean-variance-skewness portfolio performance gauging: a general shortage function and dual approach. Manage Sci 1(53):135\u2013149. https:\/\/doi.org\/10.1287\/MNSC.1060.0596","journal-title":"Manage Sci"},{"issue":"303","key":"828_CR19","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1016\/j.ejor.2022.03.037","volume":"12","author":"W Briec","year":"2022","unstructured":"Briec W, Dumas A, Kerstens K, Stenger A (2022) Generalised commensurability properties of efficiency measures: implications for productivity indicators. Eur J Oper Res 12(303):1481\u20131492. https:\/\/doi.org\/10.1016\/j.ejor.2022.03.037","journal-title":"Eur J Oper Res"},{"issue":"291","key":"828_CR20","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/J.EJOR.2020.09.044","volume":"6","author":"TS Chang","year":"2021","unstructured":"Chang TS, Tone K, Wu CH (2021) Nested dynamic network data envelopment analysis models with infinitely many decision making units for portfolio evaluation. Eur J Oper Res 6(291):766\u2013781. https:\/\/doi.org\/10.1016\/J.EJOR.2020.09.044","journal-title":"Eur J Oper Res"},{"issue":"28","key":"828_CR21","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/s00291-005-0032-1","volume":"7","author":"Z Chen","year":"2006","unstructured":"Chen Z, Lin R (2006) Mutual fund performance evaluation using data envelopment analysis with new risk measures. OR Spectr 7(28):375\u2013398. https:\/\/doi.org\/10.1007\/s00291-005-0032-1","journal-title":"OR Spectr"},{"key":"828_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2008.01.032","volume":"192","author":"WD Cook","year":"2009","unstructured":"Cook WD, Seiford LM (2009) Data envelopment analysis (DEA)-thirty years on. Eur J Oper Res 192:1\u201317. https:\/\/doi.org\/10.1016\/j.ejor.2008.01.032","journal-title":"Eur J Oper Res"},{"key":"828_CR23","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1023\/A:1018320430249","volume":"9","author":"WW Cooper","year":"1998","unstructured":"Cooper WW, Li SX, Olesen OB (1998) Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J Prod Anal 9:53\u201379","journal-title":"J Prod Anal"},{"key":"828_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-45283-8","volume-title":"Data envelopment analysis","author":"WW Cooper","year":"2007","unstructured":"Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis, 2nd edn. Springer, New York","edition":"2"},{"key":"828_CR25","doi-asserted-by":"publisher","first-page":"3018","DOI":"10.1016\/j.jbankfin.2013.04.033","volume":"37","author":"V DeMiguel","year":"2013","unstructured":"DeMiguel V, Martin-Utrera A, Nogales FJ (2013) Size matters: optimal calibration of shrinkage estimators for portfolio selection. J Bank Financ 37:3018\u20133034. https:\/\/doi.org\/10.1016\/j.jbankfin.2013.04.033","journal-title":"J Bank Financ"},{"issue":"37","key":"828_CR26","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1080\/07350015.2017.1345683","volume":"4","author":"RF Engle","year":"2019","unstructured":"Engle RF, Ledoit O, Wolf M (2019) Large dynamic covariance matrices. J Bus Econ Stat 4(37):363\u2013375. https:\/\/doi.org\/10.1080\/07350015.2017.1345683","journal-title":"J Bus Econ Stat"},{"issue":"27","key":"828_CR27","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1111\/itor.12726","volume":"5","author":"C Filippi","year":"2020","unstructured":"Filippi C, Guastaroba G, Speranza MG (2020) Conditional value-at-risk beyond finance: a survey. Int Trans Oper Res 5(27):1277\u20131319. https:\/\/doi.org\/10.1111\/itor.12726","journal-title":"Int Trans Oper Res"},{"key":"828_CR28","doi-asserted-by":"crossref","unstructured":"Fourdrinier D, Strawderman WE, Wells MT (2018) Shrinkage estimation. Springer Series in Statistics. Springer, Berlin","DOI":"10.1007\/978-3-030-02185-6"},{"key":"828_CR29","unstructured":"Fritzmeier CJ, Gelius-Dietrich G cplexAPI. Available from: https:\/\/cran.r-project.org\/src\/contrib\/Archive\/cplexAPI\/"},{"key":"828_CR30","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/j.jedc.2008.06.003","volume":"33","author":"V Golosnoy","year":"2009","unstructured":"Golosnoy V, Okhrin Y (2009) Flexible shrinkage in portfolio selection. J Econ Dyn Control 33:317\u2013328. https:\/\/doi.org\/10.1016\/j.jedc.2008.06.003","journal-title":"J Econ Dyn Control"},{"issue":"29","key":"828_CR31","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1017\/S0266466612000680","volume":"8","author":"C Gourieroux","year":"2013","unstructured":"Gourieroux C, Zako\u00efan JM (2013) Estimation-adjusted VaR. Economet Theor 8(29):735\u2013770. https:\/\/doi.org\/10.1017\/S0266466612000680","journal-title":"Economet Theor"},{"key":"828_CR32","volume-title":"Evaluating hedge fund and CTA performance: data envelopment analysis approach","author":"GN Gregoriou","year":"2005","unstructured":"Gregoriou GN, Zhu J (2005) Evaluating hedge fund and CTA performance: data envelopment analysis approach. Wiley, Hoboken"},{"key":"828_CR33","doi-asserted-by":"publisher","first-page":"10","DOI":"10.3390\/math10152808","volume":"8","author":"A Hamdi","year":"2022","unstructured":"Hamdi A, Karimi A, Mehrdoust F, Belhaouari SB (2022) Portfolio selection problem using CVaR risk measures equipped with DEA, PSO, and ICA algorithms. Mathematics 8:10. https:\/\/doi.org\/10.3390\/math10152808","journal-title":"Mathematics"},{"key":"828_CR34","doi-asserted-by":"publisher","first-page":"135","DOI":"10.2143\/AST.36.1.2014147","volume":"36","author":"U Herold","year":"2006","unstructured":"Herold U, Maurer R (2006) Portfolio choice and estimation risk: a comparison of Bbayesian to heuristic approaches. ASTIN Bullet 36:135\u2013160. https:\/\/doi.org\/10.2143\/AST.36.1.2014147","journal-title":"ASTIN Bullet"},{"key":"828_CR35","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1093\/imanum\/22.3.329","volume":"22","author":"NJ Higham","year":"2002","unstructured":"Higham NJ (2002) Computing the nearest correlation matrix\u2013a problem from finance. IMA J Numer Anal 22:329\u2013343","journal-title":"IMA J Numer Anal"},{"key":"828_CR36","unstructured":"IBM.: CPLEX 20.1.0.0. Available from: https:\/\/www.ibm.com\/products\/ilog-cplex-optimization-studio"},{"key":"828_CR37","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.econmod.2013.12.017","volume":"38","author":"J Jin","year":"2014","unstructured":"Jin J, Zhou D, Zhou P (2014) Measuring environmental performance with stochastic environmental DEA: the case of APEC economies. Econ Model 38:80\u201386. https:\/\/doi.org\/10.1016\/j.econmod.2013.12.017","journal-title":"Econ Model"},{"key":"828_CR38","doi-asserted-by":"publisher","first-page":"279","DOI":"10.2307\/2331042","volume":"21","author":"P Jorion","year":"1986","unstructured":"Jorion P (1986) Bayes-stein estimation for portfolio analysis. J Financ Quant Anal 21:279\u2013292","journal-title":"J Financ Quant Anal"},{"key":"828_CR39","doi-asserted-by":"publisher","first-page":"29","DOI":"10.21314\/JOR.2018.376","volume":"20","author":"P Kabaila","year":"2018","unstructured":"Kabaila P, Mainzer R (2018) Estimation risk for value-at-risk and expected shortfall. J Risk 20:29\u201347. https:\/\/doi.org\/10.21314\/JOR.2018.376","journal-title":"J Risk"},{"issue":"68","key":"828_CR40","doi-asserted-by":"publisher","first-page":"2047","DOI":"10.1287\/mnsc.2021.3989","volume":"3","author":"R Kan","year":"2022","unstructured":"Kan R, Wang X, Zhou G (2022) Optimal portfolio choice with estimation risk: no risk-free asset case. Manage Sci 3(68):2047\u20132068. https:\/\/doi.org\/10.1287\/mnsc.2021.3989","journal-title":"Manage Sci"},{"key":"828_CR41","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1016\/j.ejor.2013.11.006","volume":"235","author":"C Kao","year":"2014","unstructured":"Kao C, Liu ST (2014) Measuring performance improvement of Taiwanese commercial banks under uncertainty. Eur J Oper Res 235:755\u2013764. https:\/\/doi.org\/10.1016\/j.ejor.2013.11.006","journal-title":"Eur J Oper Res"},{"key":"828_CR42","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1016\/j.ejor.2018.07.051","volume":"273","author":"C Kao","year":"2019","unstructured":"Kao C, Liu ST (2019) Stochastic efficiency measures for production units with correlated data. Eur J Oper Res 273:278\u2013287. https:\/\/doi.org\/10.1016\/j.ejor.2018.07.051","journal-title":"Eur J Oper Res"},{"key":"828_CR43","first-page":"70","volume":"2","author":"V Khokhlov","year":"2016","unstructured":"Khokhlov V (2016) Conditional value-at risk for elliptical distributions. Eur J Econ Manag 2:70\u201379","journal-title":"Eur J Econ Manag"},{"key":"828_CR44","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/j.ejor.2011.08.019","volume":"216","author":"JD Lamb","year":"2012","unstructured":"Lamb JD, Tee KH (2012) Data envelopment analysis models of investment funds. Eur J Oper Res 216:687\u2013696. https:\/\/doi.org\/10.1016\/j.ejor.2011.08.019","journal-title":"Eur J Oper Res"},{"key":"828_CR45","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1016\/j.ejor.2012.07.015","volume":"223","author":"JD Lamb","year":"2012","unstructured":"Lamb JD, Tee KH (2012) Resampling DEA estimates of investment fund performance. Eur J Oper Res 223:834\u2013841. https:\/\/doi.org\/10.1016\/j.ejor.2012.07.015","journal-title":"Eur J Oper Res"},{"issue":"332","key":"828_CR46","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1007\/s10479-023-05428-w","volume":"1","author":"JD Lamb","year":"2024","unstructured":"Lamb JD, Tee KH (2024) Using stochastic frontier analysis instead of data envelopment analysis in modelling investment performance. Ann Oper Res 1(332):891\u2013907. https:\/\/doi.org\/10.1007\/s10479-023-05428-w","journal-title":"Ann Oper Res"},{"key":"828_CR47","doi-asserted-by":"publisher","first-page":"53","DOI":"10.21314\/JOR.2019.408","volume":"21","author":"JD Lamb","year":"2019","unstructured":"Lamb JD, Monville ME, Tee KH (2019) Making Cornish\u2013Fisher fit for risk measurement. J Risk 21:53\u201381. https:\/\/doi.org\/10.21314\/JOR.2019.408","journal-title":"J Risk"},{"key":"828_CR48","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1002\/mde.4090140607","volume":"14","author":"KC Land","year":"1993","unstructured":"Land KC, Lovell C, Thore S (1993) Chance-constrained data envelopment analysis. Manag Decis Econ 14:541\u2013554","journal-title":"Manag Decis Econ"},{"key":"828_CR49","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/S0047-259X(03)00096-4","volume":"88","author":"O Ledoit","year":"2004","unstructured":"Ledoit O, Wolf M (2004) A well-conditioned estimator for large-dimensional covariance matrices. J Multivar Anal 88:365\u2013411. https:\/\/doi.org\/10.1016\/S0047-259X(03)00096-4","journal-title":"J Multivar Anal"},{"key":"828_CR50","doi-asserted-by":"publisher","first-page":"4349","DOI":"10.1093\/rfs\/hhx052","volume":"30","author":"O Ledoit","year":"2017","unstructured":"Ledoit O, Wolf M (2017) Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks. Rev Financ Stud 30:4349\u20134388. https:\/\/doi.org\/10.1093\/rfs\/hhx052","journal-title":"Rev Financ Stud"},{"key":"828_CR51","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.jmva.2021.104796","volume":"11","author":"O Ledoit","year":"2021","unstructured":"Ledoit O, Wolf M (2021) Shrinkage estimation of large covariance matrices: keep it simple, statistician? J Multivar Anal 11:186. https:\/\/doi.org\/10.1016\/j.jmva.2021.104796","journal-title":"J Multivar Anal"},{"key":"828_CR52","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1016\/j.ejor.2020.06.033","volume":"288","author":"N Meade","year":"2021","unstructured":"Meade N, Beasley JE, Adcock CJ (2021) Quantitative portfolio selection: using density forecasting to find consistent portfolios. Eur J Oper Res 288:1053\u20131067. https:\/\/doi.org\/10.1016\/j.ejor.2020.06.033","journal-title":"Eur J Oper Res"},{"issue":"1","key":"828_CR53","first-page":"31","volume":"45","author":"RO Michaud","year":"2007","unstructured":"Michaud RO, Michaud R (2007) Estimation error and portfolio optimization: a resampling solution. J Invest Manag 45(1):31\u201342","journal-title":"J Invest Manag"},{"key":"828_CR54","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1016\/j.ejor.2021.11.036","volume":"301","author":"E Mynbayeva","year":"2022","unstructured":"Mynbayeva E, Lamb JD, Zhao Y (2022) Why estimation alone causes Markowitz portfolio selection to fail and what we might do about it. Eur J Oper Res 301:694\u2013707. https:\/\/doi.org\/10.1016\/j.ejor.2021.11.036","journal-title":"Eur J Oper Res"},{"key":"828_CR55","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1109\/TVLSI.2007.912191","volume":"16","author":"S Nadarajah","year":"2008","unstructured":"Nadarajah S, Kotz S (2008) Exact distribution of the max\/min of two Gaussian random variables. IEEE Trans Very Large Scale Integr 16:210\u2013212","journal-title":"IEEE Trans Very Large Scale Integr"},{"key":"828_CR56","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.ejor.2015.07.058","volume":"251","author":"OB Olesen","year":"2016","unstructured":"Olesen OB, Petersen NC (2016) Stochastic data envelopment analysis\u2013a review. Eur J Oper Res 251:2\u201321. https:\/\/doi.org\/10.1016\/j.ejor.2015.07.058","journal-title":"Eur J Oper Res"},{"key":"828_CR57","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1057\/palgrave.jors.2601768","volume":"55","author":"M Portela","year":"2004","unstructured":"Portela M, Thanassoulis E, Simpson G (2004) Negative data in DEA: a directional distance approach applied to bank branches. J Oper Res Soc 55:1111\u20131121. https:\/\/doi.org\/10.1057\/palgrave.jors.2601768","journal-title":"J Oper Res Soc"},{"key":"828_CR58","unstructured":"R Core Team.: R: a language and environment for statistical computing. Available from: https:\/\/www.r-project.org\/"},{"key":"828_CR59","unstructured":"Ramprasad P nlshrink: non-linear shrinkage estimation of population eigenvalues and covariance matrices. Available from: https:\/\/cran.r-project.org\/package=nlshrink"},{"issue":"319","key":"828_CR60","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1016\/J.EJOR.2024.06.013","volume":"11","author":"T Ren","year":"2024","unstructured":"Ren T, Kerstens K, Kumar S (2024) Risk-aversion versus risk-loving preferences in nonparametric frontier-based fund ratings: a buy-and-hold backtesting strategy. Eur J Oper Res 11(319):332\u2013344. https:\/\/doi.org\/10.1016\/J.EJOR.2024.06.013","journal-title":"Eur J Oper Res"},{"key":"828_CR61","doi-asserted-by":"publisher","first-page":"21","DOI":"10.2307\/1165345","volume":"2","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar RT, Uryasev S (1997) Optimization of conditional value-at-risk. J Risk 2:21\u201341. https:\/\/doi.org\/10.2307\/1165345","journal-title":"J Risk"},{"issue":"31","key":"828_CR62","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s11123-008-0119-1","volume":"4","author":"RR Russell","year":"2009","unstructured":"Russell RR, Schworm W (2009) Axiomatic foundations of efficiency measurement on data-generated technologies. J Prod Anal 4(31):77\u201386. https:\/\/doi.org\/10.1007\/s11123-008-0119-1","journal-title":"J Prod Anal"},{"key":"828_CR63","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1287\/mnsc.44.1.49","volume":"44","author":"L Simar","year":"1998","unstructured":"Simar L, Wilson PW (1998) Sensitivity analysis of efficiency Scores: how to bootstrap in nonparametric frontier models. Manage Sci 44:49\u201361. https:\/\/doi.org\/10.1287\/mnsc.44.1.49","journal-title":"Manage Sci"},{"key":"828_CR64","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1080\/02664760050081951","volume":"27","author":"L Simar","year":"2000","unstructured":"Simar L, Wilson PW (2000) A general methodology for bootstrapping in non-parametric frontier models. J Appl Stat 27:779\u2013802. https:\/\/doi.org\/10.1080\/02664760050081951","journal-title":"J Appl Stat"},{"issue":"36","key":"828_CR65","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11123-010-0170-6","volume":"8","author":"L Simar","year":"2011","unstructured":"Simar L, Zelenyuk V (2011) Stochastic FDH\/DEA estimators for frontier analysis. J Prod Anal 8(36):1\u201320. https:\/\/doi.org\/10.1007\/s11123-010-0170-6","journal-title":"J Prod Anal"},{"key":"828_CR66","doi-asserted-by":"crossref","unstructured":"Stein C (1955) Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proceedings of the 3rd Berkeley symposium on probability and statistics, vol\u00a01, pp 197\u2013208","DOI":"10.1525\/9780520313880-018"},{"key":"828_CR67","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1214\/aos\/1176342412","volume":"1","author":"SM Stigler","year":"1973","unstructured":"Stigler SM (1973) The asymptotic distribution of the trimmed mean. Ann Stat 1:472\u2013477","journal-title":"Ann Stat"},{"key":"828_CR68","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1177\/096228029700600202","volume":"6","author":"SM Stigler","year":"1997","unstructured":"Stigler SM (1997) Regression towards the mean, historically considered. Stat Methods Med Res 6:103\u2013114","journal-title":"Stat Methods Med Res"},{"key":"828_CR69","doi-asserted-by":"publisher","first-page":"1519","DOI":"10.1016\/S0378-4266(02)00272-8","volume":"26","author":"D Tasche","year":"2002","unstructured":"Tasche D (2002) Expected shortfall and beyond. J Bank Financ 26:1519\u20131533. https:\/\/doi.org\/10.1016\/S0378-4266(02)00272-8","journal-title":"J Bank Financ"},{"key":"828_CR70","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.spc.2019.11.001","volume":"21","author":"M Tavassoli","year":"2020","unstructured":"Tavassoli M, Saen RF, Zanjirani DM (2020) Assessing sustainability of suppliers: a novel stochastic-fuzzy DEA model. Sustain Prod Consum 21:78\u201391. https:\/\/doi.org\/10.1016\/j.spc.2019.11.001","journal-title":"Sustain Prod Consum"},{"key":"828_CR71","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1016\/j.ejor.2016.09.033","volume":"258","author":"MG Tsionas","year":"2017","unstructured":"Tsionas MG (2017) Microfoundations for stochastic frontiers. Eur J Oper Res 258:1165\u20131170. https:\/\/doi.org\/10.1016\/j.ejor.2016.09.033","journal-title":"Eur J Oper Res"},{"key":"828_CR72","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.omega.2009.02.003","volume":"38","author":"EG Tsionas","year":"2010","unstructured":"Tsionas EG, Papadakis EN (2010) A Bayesian approach to statistical inference in stochastic DEA. Omega 38:309\u2013314. https:\/\/doi.org\/10.1016\/j.omega.2009.02.003","journal-title":"Omega"},{"issue":"287","key":"828_CR73","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1016\/j.ejor.2020.04.020","volume":"12","author":"Z Wang","year":"2020","unstructured":"Wang Z, Crook J, Andreeva G (2020) Reducing estimation risk using a Bayesian posterior distribution approach: application to stress testing mortgage loan default. Eur J Oper Res 12(287):725\u2013738. https:\/\/doi.org\/10.1016\/j.ejor.2020.04.020","journal-title":"Eur J Oper Res"},{"key":"828_CR74","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1051\/ro\/2016065","volume":"52","author":"P Wanke","year":"2018","unstructured":"Wanke P, Barros CP, Emrouznejad A (2018) A comparison between stochastic DEA and fuzzy DEA approaches: revisiting efficiency in Angolan banks. RAIRO Oper Res 52:285\u2013303. https:\/\/doi.org\/10.1051\/ro\/2016065","journal-title":"RAIRO Oper Res"},{"issue":"103","key":"828_CR75","doi-asserted-by":"publisher","first-page":"102357","DOI":"10.1016\/j.omega.2020.102357","volume":"9","author":"H Xiao","year":"2021","unstructured":"Xiao H, Ren T, Zhou Z, Liu W (2021) Parameter uncertainty in estimation of portfolio efficiency: evidence from an interval diversification-consistent DEA approach. Omega 9(103):102357. https:\/\/doi.org\/10.1016\/j.omega.2020.102357","journal-title":"Omega"},{"key":"828_CR76","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1080\/03155986.2022.2051385","volume":"60","author":"H Xiao","year":"2022","unstructured":"Xiao H, Liu X, Ren T, Zhou Z (2022) Measuring the dynamic efficiency of socially responsible investment funds: evidence from dynamic network DEA with diversification. Infor Inf Syst Oper Res 60:531\u2013557. https:\/\/doi.org\/10.1080\/03155986.2022.2051385","journal-title":"Infor Inf Syst Oper Res"},{"issue":"56","key":"828_CR77","doi-asserted-by":"publisher","first-page":"2367","DOI":"10.1051\/ro\/2022114","volume":"7","author":"H Xiao","year":"2022","unstructured":"Xiao H, Liu X, Ren T, Zhou Z (2022) Estimation of portfolio efficiency via stochastic DEA. RAIRO Oper Res 7(56):2367\u20132387. https:\/\/doi.org\/10.1051\/ro\/2022114","journal-title":"RAIRO Oper Res"},{"key":"828_CR78","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1134\/S1995080217010218","volume":"38","author":"N Zahra","year":"2017","unstructured":"Zahra N, Lisawadi S, Ahmed SE (2017) Improved estimation of kurtosis parameters for two multivariate populations. Lobachevskii J Math 38:110\u2013115. https:\/\/doi.org\/10.1134\/S1995080217010218","journal-title":"Lobachevskii J Math"},{"key":"828_CR79","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s00186-008-0234-9","volume":"70","author":"H Zheng","year":"2009","unstructured":"Zheng H (2009) Efficient frontier of utility and CVaR. Math Methods Oper Res 70:129\u2013148. https:\/\/doi.org\/10.1007\/s00186-008-0234-9","journal-title":"Math Methods Oper Res"},{"issue":"6","key":"828_CR80","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.jmse.2021.02.004","volume":"12","author":"Z Zhou","year":"2021","unstructured":"Zhou Z, Sun W, Xiao H, Jin Q, Liu W (2021) Stochastic leader\u2013follower DEA models for two-stage systems. J Manag Sci Eng 12(6):413\u2013434. https:\/\/doi.org\/10.1016\/j.jmse.2021.02.004","journal-title":"J Manag Sci Eng"}],"container-title":["OR Spectrum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-025-00828-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00291-025-00828-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-025-00828-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T11:20:01Z","timestamp":1777548001000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00291-025-00828-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,22]]},"references-count":80,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["828"],"URL":"https:\/\/doi.org\/10.1007\/s00291-025-00828-9","relation":{},"ISSN":["0171-6468","1436-6304"],"issn-type":[{"value":"0171-6468","type":"print"},{"value":"1436-6304","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,22]]},"assertion":[{"value":"20 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}