{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,29]],"date-time":"2026-10-29T11:44:38Z","timestamp":1793274278838,"version":"4.5.0"},"reference-count":52,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T00:00:00Z","timestamp":1761091200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"},{"start":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T00:00:00Z","timestamp":1761091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/tdm\/tdmrep-policy.json"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12561051"],"award-info":[{"award-number":["12561051"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72525001"],"award-info":[{"award-number":["72525001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72495124"],"award-info":[{"award-number":["72495124"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:p>\n                    We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a\n                    <jats:italic>J<\/jats:italic>\n                    -fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some settings and assigning all weight to the correctly specified models if such models exist in the candidate set. Moreover, consistency properties of the optimal weights and model averaging estimators are established. A simulation study and an empirical example demonstrate the superiority of the proposed estimator over other methods.\n                  <\/jats:p>","DOI":"10.1017\/s0266466625100200","type":"journal-article","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T08:08:49Z","timestamp":1761120529000},"page":"1194-1227","source":"Crossref","is-referenced-by-count":1,"title":["AVERAGING ESTIMATORS OF HETEROGENEOUS TREATMENT EFFECTS UNDER ADDITIVE MODELS"],"prefix":"10.1017","volume":"42","author":[{"given":"Na","family":"Li","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00xyeez13","id-type":"ROR","asserted-by":"publisher"}],"name":"Kunming University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Fei","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04rhev598","id-type":"ROR","asserted-by":"publisher"}],"name":"Yunnan University of Finance and Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3618-3083","authenticated-orcid":false,"given":"Yuhong","family":"Yang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03cve4549","id-type":"ROR","asserted-by":"publisher"}],"name":"Tsinghua University and Beijing Institute of Mathematical Sciences and Applications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinyu","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05t6hvr95","id-type":"ROR","asserted-by":"publisher"}],"name":"Chinese Academy of Sciences and University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,10,22]]},"reference":[{"key":"S0266466625100200_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.07.002"},{"key":"S0266466625100200_r32","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/10618600.2017.1356325","article-title":"Estimating individual treatment effect in observational data using random forest methods","volume":"27","author":"Min","year":"2018","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"S0266466625100200_r28","doi-asserted-by":"publisher","DOI":"10.1111\/ectj.12063"},{"key":"S0266466625100200_r46","first-page":"1281","article-title":"Consistent variable selection in additive models","volume":"19","author":"Xue","year":"2009","journal-title":"Statistica Sinica"},{"key":"S0266466625100200_r20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2022.01.009"},{"key":"S0266466625100200_r31","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12023"},{"key":"S0266466625100200_r49","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2015.1115762"},{"key":"S0266466625100200_r34","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1034276626"},{"key":"S0266466625100200_r1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00655.x"},{"key":"S0266466625100200_r21","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS932"},{"key":"S0266466625100200_r26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2018.10.007"},{"key":"S0266466625100200_r40","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"S0266466625100200_r12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.06.019"},{"key":"S0266466625100200_r5","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxq060"},{"key":"S0266466625100200_r11","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00785.x"},{"key":"S0266466625100200_r43","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012031"},{"key":"S0266466625100200_r16","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOAS593"},{"key":"S0266466625100200_r30","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2019.1609974"},{"key":"S0266466625100200_r41","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325632"},{"key":"S0266466625100200_r42","volume-title":"Spline functions: Basic theory","author":"Schumaker","year":"1981"},{"key":"S0266466625100200_r9","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2011.tm09779"},{"key":"S0266466625100200_r18","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1804597116"},{"key":"S0266466625100200_r6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2006.00567.x"},{"key":"S0266466625100200_r2","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.07333"},{"key":"S0266466625100200_r22","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1475"},{"key":"S0266466625100200_r33","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asaa076"},{"key":"S0266466625100200_r52","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2022.2047508"},{"key":"S0266466625100200_r37","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2009.00718.x"},{"key":"S0266466625100200_r17","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12736"},{"key":"S0266466625100200_r13","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1009212519"},{"key":"S0266466625100200_r38","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12043"},{"key":"S0266466625100200_r10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2020.09.008"},{"key":"S0266466625100200_r15","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS781"},{"key":"S0266466625100200_r35","unstructured":"Qiu, Y. , Xie, T. , Yu, J. , & Zhang, X. (2020). Mallows-type averaging machine learning techniques. Working Paper."},{"key":"S0266466625100200_r8","doi-asserted-by":"publisher","DOI":"10.1002\/asmb.2898"},{"key":"S0266466625100200_r39","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466618000397"},{"key":"S0266466625100200_r51","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-023-00876-4"},{"key":"S0266466625100200_r24","first-page":"1187","article-title":"Semiparametric model averaging prediction for lifetime data via hazards regression","volume":"70","author":"Li","year":"2021","journal-title":"Journal of the Royal Statistical Society: Series C (Applied Statistics)"},{"key":"S0266466625100200_r48","doi-asserted-by":"publisher","DOI":"10.1080\/24754269.2022.2105486"},{"key":"S0266466625100200_r45","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1319839"},{"key":"S0266466625100200_r7","doi-asserted-by":"publisher","DOI":"10.1257\/aer.20221167"},{"key":"S0266466625100200_r29","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asw051"},{"key":"S0266466625100200_r50","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ast052"},{"key":"S0266466625100200_r19","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOS1071"},{"key":"S0266466625100200_r14","first-page":"1","article-title":"Optimal parameter-transfer learning by semiparametric model averaging","volume":"24","author":"Hu","year":"2023","journal-title":"Journal of Machine Learning Research"},{"key":"S0266466625100200_r4","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347115"},{"key":"S0266466625100200_r44","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349548"},{"key":"S0266466625100200_r36","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2022.2118126"},{"key":"S0266466625100200_r3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1510489113"},{"key":"S0266466625100200_r25","first-page":"401","article-title":"Frequentist model averaging for the nonparametric additive model","volume":"33","author":"Liao","year":"2023","journal-title":"Statistica Sinica"},{"key":"S0266466625100200_r23","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1790375"},{"key":"S0266466625100200_r47","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1999.1884"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466625100200","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466625100200","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,29]],"date-time":"2026-10-29T10:45:37Z","timestamp":1793270737000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466625100200\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,22]]},"references-count":52,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["S0266466625100200"],"URL":"https:\/\/doi.org\/10.1017\/s0266466625100200","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,22]]}}}