{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T03:56:24Z","timestamp":1774238184120,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T00:00:00Z","timestamp":1774224000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T00:00:00Z","timestamp":1774224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Data Sci Anal"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1007\/s41060-025-01002-8","type":"journal-article","created":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T03:15:02Z","timestamp":1774235702000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluating credit lending fairness with binarized continuous variables in SAFE metrics"],"prefix":"10.1007","volume":"22","author":[{"given":"Lunshuai","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,23]]},"reference":[{"key":"1002_CR1","doi-asserted-by":"crossref","unstructured":"Babaei, G., Giudici, P., Wu, L.: Explainable fairness in mortgage lending. In: The 3rd World Conference on eXplainable Artificial Intelligence (XAI-2025) (2025b)","DOI":"10.1007\/978-3-032-08330-2_18"},{"issue":"1","key":"1002_CR2","first-page":"1","volume":"7","author":"DK Horne","year":"1994","unstructured":"Horne, D.K.: Evaluating the role of race in mortgage lending. FDIC Bank. Rev. 7(1), 1\u201316 (1994)","journal-title":"FDIC Bank. Rev."},{"issue":"3","key":"1002_CR3","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1177\/107808749402900308","volume":"29","author":"CL Leven","year":"1994","unstructured":"Leven, C.L., Sykuta, M.E.: The importance of race in home mortgage loan approvals. Urban Affairs Quart. 29(3), 479\u2013489 (1994)","journal-title":"Urban Affairs Quart."},{"issue":"1","key":"1002_CR4","first-page":"115","volume":"6","author":"BW Ambrose","year":"1995","unstructured":"Ambrose, B.W., Hughes, W.T., Jr., Simmons, P.: Policy issues concerning racial and ethnic differences in home loan rejection rates. J. Hous. Res. 6(1), 115\u2013135 (1995)","journal-title":"J. Hous. Res."},{"key":"1002_CR5","first-page":"117","volume":"7","author":"SL Ross","year":"1996","unstructured":"Ross, S.L.: Mortgage lending discrimination and racial differences in loan default. J. Hous. Res. 7, 117\u2013126 (1996)","journal-title":"J. Hous. Res."},{"issue":"1","key":"1002_CR6","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1023\/A:1007927123582","volume":"11","author":"DK Horne","year":"1997","unstructured":"Horne, D.K.: Mortgage lending, race, and model specification. J. Financ. Serv. Res. 11(1), 43\u201368 (1997)","journal-title":"J. Financ. Serv. Res."},{"issue":"2","key":"1002_CR7","first-page":"277","volume":"8","author":"SL Ross","year":"1997","unstructured":"Ross, S.L.: Mortgage lending discrimination and racial differences in loan default: a simulation approach. J. Hous. Res. 8(2), 277\u2013297 (1997)","journal-title":"J. Hous. Res."},{"issue":"4","key":"1002_CR8","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1080\/00380237.1998.10571116","volume":"31","author":"KF Gotham","year":"1998","unstructured":"Gotham, K.F.: Race, mortgage lending and loan rejections in a US city. Sociol. Focus 31(4), 391\u2013405 (1998)","journal-title":"Sociol. Focus"},{"issue":"1","key":"1002_CR9","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1111\/j.1465-7295.2000.tb00009.x","volume":"38","author":"RE Martin","year":"2000","unstructured":"Martin, R.E., Hill, R.C.: Loan performance and race. Econ. Inq. 38(1), 136\u2013150 (2000)","journal-title":"Econ. Inq."},{"issue":"2","key":"1002_CR10","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1080\/10511482.2013.771788","volume":"23","author":"JW Faber","year":"2013","unstructured":"Faber, J.W.: Racial dynamics of subprime mortgage lending at the peak. Hous. Policy Debate 23(2), 328\u2013349 (2013)","journal-title":"Hous. Policy Debate"},{"key":"1002_CR11","doi-asserted-by":"crossref","unstructured":"Perry, V.G.: A loan at last: race and racism in mortgage lending. In: Race in the marketplace: Crossing critical boundaries, pp. 173\u2013192 (2019)","DOI":"10.1007\/978-3-030-11711-5_11"},{"issue":"3","key":"1002_CR12","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1111\/rode.12607","volume":"24","author":"R Gonzales Martinez","year":"2020","unstructured":"Gonzales Martinez, R., Aguilera-Lizarazu, G., Rojas-Hosse, A., Aranda Blanco, P.: The interaction effect of gender and ethnicity in loan approval: a Bayesian estimation with data from a laboratory field experiment. Rev. Dev. Econ. 24(3), 726\u2013749 (2020)","journal-title":"Rev. Dev. Econ."},{"issue":"4","key":"1002_CR13","first-page":"77","volume":"11","author":"JA Smith","year":"2023","unstructured":"Smith, J.A., Fulgham, G.G.: Investigating racial\/ethnic disparities in loan approval: a Mississippi perspective. Am. Res. J. Econ. Finance Manag. 11(4), 77\u201393 (2023)","journal-title":"Am. Res. J. Econ. Finance Manag."},{"issue":"1","key":"1002_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/rfs\/hhac029","volume":"36","author":"AW Butler","year":"2023","unstructured":"Butler, A.W., Mayer, E.J., Weston, J.P.: Racial disparities in the auto loan market. Rev. Financ. Stud. 36(1), 1\u201341 (2023)","journal-title":"Rev. Financ. Stud."},{"key":"1002_CR15","unstructured":"Giudici, P.: Safe machine learning. Statistics, pp. 1\u20135 (2024)"},{"key":"1002_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121220","volume":"235","author":"P Giudici","year":"2024","unstructured":"Giudici, P., Centurelli, M., Turchetta, S.: Artificial intelligence risk measurement. Expert Syst. Appl. 235, 121220 (2024)","journal-title":"Expert Syst. Appl."},{"key":"1002_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.frl.2023.104088","volume":"56","author":"P Giudici","year":"2023","unstructured":"Giudici, P., Raffinetti, E.: Safe artificial intelligence in finance. Financ. Res. Lett. 56, 104088 (2023)","journal-title":"Financ. Res. Lett."},{"issue":"Suppl 2","key":"1002_CR18","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s11135-023-01613-y","volume":"57","author":"E Raffinetti","year":"2023","unstructured":"Raffinetti, E.: A rank graduation accuracy measure to mitigate artificial intelligence risks. Qual. Quant. 57(Suppl 2), 131\u2013150 (2023)","journal-title":"Qual. Quant."},{"key":"1002_CR19","doi-asserted-by":"crossref","unstructured":"Giudici, P., Raffinetti, E.: RGA: a unified measure of predictive accuracy. Advances in Data Analysis and Classification, pp. 1\u201327 (2024)","DOI":"10.1007\/s11634-023-00574-2"},{"key":"1002_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.125239","volume":"259","author":"G Babaei","year":"2025","unstructured":"Babaei, G., Giudici, P., Raffinetti, E.: A rank graduation box for safe AI. Expert Syst. Appl. 259, 125239 (2025)","journal-title":"Expert Syst. Appl."},{"issue":"6","key":"1002_CR21","doi-asserted-by":"publisher","first-page":"1283","DOI":"10.1080\/02331888.2024.2419420","volume":"58","author":"A Spelta","year":"2024","unstructured":"Spelta, A., Raffinetti, E.: Evaluating safe AI principles using Wasserstein distance: a comparative study of machine learning models. Statistics 58(6), 1283\u20131303 (2024)","journal-title":"Statistics"},{"issue":"3","key":"1002_CR22","doi-asserted-by":"publisher","first-page":"442","DOI":"10.3390\/math13030442","volume":"13","author":"TD Phan","year":"2025","unstructured":"Phan, T.D., Giudici, P.: Sustainability, accuracy, fairness, and explainability (safe) machine learning in quantitative trading. Mathematics 13(3), 442 (2025)","journal-title":"Mathematics"},{"key":"1002_CR23","doi-asserted-by":"publisher","first-page":"1566197","DOI":"10.3389\/frai.2025.1566197","volume":"8","author":"P Giudici","year":"2025","unstructured":"Giudici, P., Wu, L.: Sustainable artificial intelligence in finance: impact of ESG factors. Front. Artif. Intell. 8, 1566197 (2025)","journal-title":"Front. Artif. Intell."},{"key":"1002_CR24","doi-asserted-by":"crossref","unstructured":"Wu, L.: A review of the transition from Shapley values and Shap values to RGE. Statistics, pp. 1\u201323 (2025)","DOI":"10.1080\/02331888.2025.2487853"},{"key":"1002_CR25","doi-asserted-by":"crossref","unstructured":"Shapley, L.S.: A value for n-person games, 2 (1953)","DOI":"10.1515\/9781400881970-018"},{"key":"1002_CR26","unstructured":"Lundberg, S.M., Lee, S.: A unified approach to interpreting model predictions. Proceedings of NIPS2017, pp. 4768\u20134777 (2017)"},{"issue":"70","key":"1002_CR27","doi-asserted-by":"publisher","first-page":"209","DOI":"10.2307\/2276207","volume":"9","author":"M Lorenz","year":"1905","unstructured":"Lorenz, M.: Methods of measuring the concentration wealth. Publ. Am. Stat. Assoc. 9(70), 209\u2013219 (1905). https:\/\/doi.org\/10.2307\/2276207","journal-title":"Publ. Am. Stat. Assoc."},{"key":"1002_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2022.101696","volume":"74","author":"H Tong","year":"2023","unstructured":"Tong, H.: Functional linear regression with Huber loss. J. Complex. 74, 101696 (2023)","journal-title":"J. Complex."},{"issue":"1","key":"1002_CR29","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1214\/aoms\/1177703732","volume":"35","author":"PJ Huber","year":"1964","unstructured":"Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Stat. 35(1), 73\u2013101 (1964)","journal-title":"Ann. Math. Stat."},{"key":"1002_CR30","first-page":"389","volume":"39","author":"M Ausloos","year":"2009","unstructured":"Ausloos, M., Mi\u015bkiewicz, J.: Introducing the q-Theil index. Braz. J. Phys. 39, 389\u2013395 (2009)","journal-title":"Braz. J. Phys."},{"key":"1002_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.114104","volume":"167","author":"P Giudici","year":"2021","unstructured":"Giudici, P., Raffinetti, E.: Shapley-Lorenz explainable artificial intelligence. Expert Syst. Appl. 167, 114104 (2021)","journal-title":"Expert Syst. Appl."}],"container-title":["International Journal of Data Science and Analytics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-025-01002-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41060-025-01002-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-025-01002-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T03:15:07Z","timestamp":1774235707000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41060-025-01002-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,23]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,12]]}},"alternative-id":["1002"],"URL":"https:\/\/doi.org\/10.1007\/s41060-025-01002-8","relation":{},"ISSN":["2364-415X","2364-4168"],"issn-type":[{"value":"2364-415X","type":"print"},{"value":"2364-4168","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,23]]},"assertion":[{"value":"3 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"113"}}