{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T09:16:45Z","timestamp":1771492605214,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"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":["J Syst Sci Complex"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s11424-023-1172-6","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T16:03:21Z","timestamp":1677686601000},"page":"412-432","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Least Squares Model Averaging for Two Non-Nested Linear Models"],"prefix":"10.1007","volume":"36","author":[{"given":"Yan","family":"Gao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianfa","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohua","family":"Zou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,1]]},"reference":[{"issue":"6","key":"1172_CR1","first-page":"97","volume":"28","author":"X Zhang","year":"2011","unstructured":"Zhang X and Zou G, Model averaging method and its application in forecast, Statistical Research, 2011, 28(6): 97\u2013102 (in Chinese).","journal-title":"Statistical Research"},{"key":"1172_CR2","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.jeconom.2015.07.006","volume":"192","author":"Y Gao","year":"2016","unstructured":"Gao Y, Zhang X, Wang S, et al., Model averaging based on leave-subject-out cross-validation, Journal of Econometrics, 2016, 192: 139\u2013151.","journal-title":"Journal of Econometrics"},{"issue":"4","key":"1172_CR3","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1080\/23249935.2015.1137652","volume":"12","author":"Y Gao","year":"2016","unstructured":"Gao Y, Luo M, and Zou G, Forecasting with model selection or model averaging: A case study for monthly container port throughput, Transportmetrica A: Transport Science, 2016, 12(4): 366\u2013384.","journal-title":"Transportmetrica A: Transport Science"},{"issue":"2","key":"1172_CR4","first-page":"210","volume":"38","author":"S Zhao","year":"2018","unstructured":"Zhao S and Zhou J, Forecasting Chinese ports container throughput: A combining time series, Journal of Systems Science and Mathematical Sciences, 2018, 38(2): 210\u2013219 (in Chinese).","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"issue":"4","key":"1172_CR5","first-page":"729","volume":"40","author":"Y Gao","year":"2020","unstructured":"Gao Y, Zhou J, Wang H, et al., Forecasting Chinese ports container throughput based on the jackknife model averaging method, Journal of Systems Science and Mathematical Sciences, 2020, 40(4): 729\u2013737 (in Chinese).","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"issue":"2","key":"1172_CR6","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s11424-018-7093-0","volume":"32","author":"X Zhang","year":"2019","unstructured":"Zhang X, Zheng Y, and Wang S, A demand forecasting method based on stochastic frontier analysis and model average: An application in air travel demand forecasting, Journal of Systems Science and Complexity, 2019, 32(2): 167\u2013185.","journal-title":"Journal of Systems Science and Complexity"},{"key":"1172_CR7","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1214\/ss\/1009212519","volume":"14","author":"J A Hoeting","year":"1999","unstructured":"Hoeting J A, Madigan D, Raftery A E, et al., Bayesian model averaging: A tutorial, Statistical Science, 1999, 14: 382\u2013417.","journal-title":"Statistical Science"},{"key":"1172_CR8","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1198\/016214503000000891","volume":"98","author":"A E Raftery","year":"2003","unstructured":"Raftery A E and Zheng Y, Long-run performance of Bayesian model averaging, Journal of the American Statistical Association, 2003, 98: 931\u2013938.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR9","doi-asserted-by":"publisher","first-page":"603","DOI":"10.2307\/2533961","volume":"53","author":"S T Buckland","year":"1997","unstructured":"Buckland S T, Burnhamn K P, and Augustin N H, Model selection: An integral part of inference, Biometrics, 1997, 53: 603\u2013618.","journal-title":"Biometrics"},{"issue":"1","key":"1172_CR10","first-page":"76","volume":"28","author":"Y Yang","year":"1999","unstructured":"Yang Y, Mixing strategies for density estimation, Annals of Statistics, 1999, 28(1): 76\u201387.","journal-title":"Annals of Statistics"},{"key":"1172_CR11","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1198\/016214503000000828","volume":"98","author":"N L Hjort","year":"2003","unstructured":"Hjort N L and Claeskens G, Frequentist model average estimators, Journal of the American Statistical Association, 2003, 98: 879\u2013899.","journal-title":", Journal of the American Statistical Association"},{"key":"1172_CR12","doi-asserted-by":"publisher","first-page":"1202","DOI":"10.1198\/016214505000000088","volume":"100","author":"Z Yuan","year":"2005","unstructured":"Yuan Z and Yang Y, Combining linear regression models: When and how, Journal of the American Statistical Association, 2005, 100: 1202\u20131214.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR13","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1111\/j.1468-0262.2007.00785.x","volume":"75","author":"B E Hansen","year":"2007","unstructured":"Hansen B E, Least squares model averaging, Econometrica, 2007, 75: 1175\u20131189.","journal-title":"Econometrica"},{"key":"1172_CR14","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1017\/S0266466609990235","volume":"25","author":"B E Hansen","year":"2009","unstructured":"Hansen B E, Averaging estimators for regressions with a possible structural break, Econometric Theory, 2009, 25: 1498\u20131514.","journal-title":"Econometric Theory"},{"key":"1172_CR15","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.jeconom.2010.03.022","volume":"158","author":"B E Hansen","year":"2010","unstructured":"Hansen B E, Averaging estimators for autoregressions with a near unit root, Journal of Econometrics, 2010, 158: 142\u2013155.","journal-title":"Journal of Econometrics"},{"key":"1172_CR16","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1111\/ectj.12009","volume":"16","author":"Q Liu","year":"2013","unstructured":"Liu Q and Okui R, Heteroskedasticity-robust Cp model averaging, Econometrics Journal, 2013, 16: 463\u2013472.","journal-title":"Econometrics Journal"},{"key":"1172_CR17","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1080\/01621459.2013.838168","volume":"109","author":"T Ando","year":"2014","unstructured":"Ando T and Li K, A model-averaging approach for high-dimensional regression, Journal of the American Statistical Association, 2014, 109: 254\u2013265.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR18","doi-asserted-by":"publisher","first-page":"2654","DOI":"10.1214\/17-AOS1538","volume":"45","author":"T Ando","year":"2017","unstructured":"Ando T and Li K, A weight-relaxed model averaging approach for high-dimensional generalized linear models, Annals of Statistics, 2017, 45: 2654\u20132679.","journal-title":"Annals of Statistics"},{"key":"1172_CR19","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/j.jeconom.2009.10.030","volume":"156","author":"A T K Wan","year":"2010","unstructured":"Wan A T K, Zhang X, and Zou G, Least squares model averaging by Mallows criterion, Journal of Econometrics, 2010, 156: 277\u2013283.","journal-title":"Journal of Econometrics"},{"key":"1172_CR20","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1017\/S0266466620000055","volume":"37","author":"X Zhang","year":"2021","unstructured":"Zhang X, A new study on asymptotic optimality of least squares model averaging, Econometric Theory, 2021, 37: 388\u2013407.","journal-title":"Econometric Theory"},{"issue":"495","key":"1172_CR21","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1198\/jasa.2011.tm09478","volume":"106","author":"H Liang","year":"2011","unstructured":"Liang H, Zou G, Wan A T K, et al., On optimal weight choice for Frequentist model average estimators, Journal of the American Statistical Association, 2011, 106(495): 1053\u20131066.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR22","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.jeconom.2011.06.019","volume":"167","author":"B E Hansen","year":"2012","unstructured":"Hansen B E and Racine J S, Jackknife model averaging, Journal of Econometrics, 2012, 167: 38\u201346.","journal-title":"Journal of Econometrics"},{"key":"1172_CR23","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.jeconom.2013.01.004","volume":"174","author":"X Zhang","year":"2013","unstructured":"Zhang X, Wan A T K, and Zou G, Model averaging by jackknife criterion in models with dependent data, Journal of Econometrics, 2013, 174: 82\u201394.","journal-title":"Journal of Econometrics"},{"key":"1172_CR24","first-page":"1583","volume":"25","author":"X Zhang","year":"2015","unstructured":"Zhang X, Zou G, and Carroll R J, Model averaging based on Kullback-Leibler distance, Statistica Sinica, 2015, 25: 1583\u20131598.","journal-title":"Statistica Sinica"},{"issue":"6","key":"1172_CR25","first-page":"679","volume":"38","author":"J Zhou","year":"2018","unstructured":"Zhou J and Zhao S, Frequentist model averaging for high dimensional poisson models, Journal of Systems Science and Mathematical Sciences, 2018, 38(6): 679\u2013687 (in Chinese).","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"issue":"6","key":"1172_CR26","doi-asserted-by":"publisher","first-page":"2013","DOI":"10.1007\/s11424-020-9343-1","volume":"33","author":"Z Zhao","year":"2020","unstructured":"Zhao Z and Zou G, Average estimation of semiparametric models for high-dimensional longitudinal data, Journal of Systems Science and Complexity, 2020, 33(6): 2013\u20132047.","journal-title":"Journal of Systems Science and Complexity"},{"issue":"7","key":"1172_CR27","first-page":"1297","volume":"40","author":"X Chen","year":"2020","unstructured":"Chen X and Zhao Z, Model average for high-dimensional longitudinal data, Journal of Systems Science and Mathematical Sciences, 2020, 40(7): 1297\u20131324 (in Chinese).","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"1172_CR28","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.econlet.2015.03.017","volume":"130","author":"X Zhang","year":"2015","unstructured":"Zhang X, Consistency of model averaging estimators, Economics Letters, 2015, 130: 120\u2013123.","journal-title":"Economics Letters"},{"key":"1172_CR29","volume-title":"Optimal designs for model averaging in non-nested models","author":"K Alhorn","year":"2019","unstructured":"Alhorn K, Dette H, and Schorning K, Optimal designs for model averaging in non-nested models, 2019, Working paper."},{"key":"1172_CR30","doi-asserted-by":"publisher","first-page":"109586","DOI":"10.1016\/j.econlet.2020.109586","volume":"196","author":"F Fang","year":"2020","unstructured":"Fang F and Liu M, Limit of the optimal weight in least squares model averaging with non-nested models, Economics Letters, 2020, 196: 109586.","journal-title":"Economics Letters"},{"issue":"1","key":"1172_CR31","doi-asserted-by":"publisher","first-page":"114","DOI":"10.2307\/2533319","volume":"51","author":"P Royston","year":"1995","unstructured":"Royston P and Thompson S G, Comparing non-nested regression models, Biometrics, 1995, 51(1): 114\u2013127.","journal-title":"Biometrics"},{"issue":"530","key":"1172_CR32","doi-asserted-by":"publisher","first-page":"972","DOI":"10.1080\/01621459.2019.1604363","volume":"115","author":"X Zhang","year":"2020","unstructured":"Zhang X, Zou G, Liang H, et al., Parsimonious model averaging with a diverging number of parameters, Journal of the American Statistical Association, 2020, 115(530): 972\u2013984.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR33","first-page":"267","volume-title":"Proceedings of the Second International Symposium on Information Theory","author":"H Akaike","year":"1973","unstructured":"Akaike H, Information theory and an extension of the maximum likelihood principle, Proceedings of the Second International Symposium on Information Theory, Eds. by Petrov B N and Csaki F, Budapest, 1973, 267\u2013281."},{"issue":"2","key":"1172_CR34","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz G, Estimating the dimension of a model, Annals of Statistics, 1978, 6(2): 461\u2013464.","journal-title":"Annals of Statistics"},{"issue":"4","key":"1172_CR35","first-page":"661","volume":"15","author":"C L Mallows","year":"1973","unstructured":"Mallows C L, Some comments on Cp, Technometrics, 1973, 15(4): 661\u2013675.","journal-title":"Technometrics"},{"issue":"1","key":"1172_CR36","first-page":"149","volume":"67","author":"G Claeskens","year":"2008","unstructured":"Claeskens G and Hjort H L, Model Selection and Model Averaging, Cambridge University Press, New York, 2008. sai][37]_McAleer M, The significance of testing empirical non-nested models, Journal of Econometrics, 1995, 67(1): 149\u2013171.","journal-title":"Model Selection and Model Averaging"},{"key":"1172_CR37","doi-asserted-by":"publisher","first-page":"781","DOI":"10.2307\/1911522","volume":"49","author":"R Davidson","year":"1981","unstructured":"Davidson R and MacKinnon J G, Several tests for model specification in the presence of alternative hypotheses, Econometrica, 1981, 49: 781\u2013793.","journal-title":"Econometrica"},{"key":"1172_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1081\/STA-100001555","volume":"30","author":"M R Watnik","year":"2001","unstructured":"Watnik M R, Johnson W O, and Bedrick E J, Nonnested linear model selection revisited, Communications in Statistics-Theory and Methods, 2001, 30: 1\u201320.","journal-title":"Communications in Statistics-Theory and Methods"},{"issue":"6","key":"1172_CR39","doi-asserted-by":"publisher","first-page":"1203","DOI":"10.1007\/s11425-014-4935-7","volume":"58","author":"X Chen","year":"2015","unstructured":"Chen X, Fan Y, Wan A, et al., Post-J test inference in non-nested linear regression models, Science China Mathematics, 2015, 58(6): 1203\u20131216.","journal-title":"Science China Mathematics"},{"key":"1172_CR40","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0167-7152(87)90020-4","volume":"5","author":"A K Bera","year":"1987","unstructured":"Bera A K and McAleer M, On exact and asymptotic tests of non-nested models, Statistics & Probability Letters, 1987, 5: 19\u201322.","journal-title":"Statistics & Probability Letters"},{"key":"1172_CR41","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"J Fan","year":"2001","unstructured":"Fan J and Li R, Variable selection via penalized likelihood and its oracle properties, Journal of the American Statistical Association, 2001, 96: 1348\u20131360.","journal-title":"Journal of the American Statistical Association"},{"key":"1172_CR42","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970128","volume-title":"Spline Models for Observational Data","author":"G Wahba","year":"1990","unstructured":"Wahba G, Spline Models for Observational Data, Society for Industrial and Applied Mathematics, Philadelphia, 1990."},{"key":"1172_CR43","series-title":"Monographs on Statistics and Applied Probability","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4473-3","volume-title":"Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach","author":"P J Green","year":"1994","unstructured":"Green P J and Silverman B W, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Volume 58 of Monographs on Statistics and Applied Probability, Chapman & Hall, London, 1994."},{"key":"1172_CR44","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani R, Regression shrinkage and selection via lasso, Journal of the Royal Statistical Society, Series B, 1996, 58: 267\u2013288.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"1172_CR45","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1080\/00401706.1995.10484371","volume":"37","author":"L Breiman","year":"1995","unstructured":"Breiman L, Better subset regression using the nonnegative garrote, Technometrics, 1995, 37: 373\u2013384.","journal-title":"Technometrics"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-023-1172-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-023-1172-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-023-1172-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T13:58:25Z","timestamp":1729000705000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-023-1172-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["1172"],"URL":"https:\/\/doi.org\/10.1007\/s11424-023-1172-6","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2]]},"assertion":[{"value":"25 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}