{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:35:30Z","timestamp":1777509330921,"version":"3.51.4"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100000155","name":"Social Sciences and Humanities Research Council of Canada","doi-asserted-by":"publisher","award":["435-2018-0275"],"award-info":[{"award-number":["435-2018-0275"]}],"id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,9,10]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem can be reformulated as MIP. We derive the nonasymptotic bound for the tail probability of the predictive performance measure. We investigate the performance of the MIP algorithm by an empirical example and Monte Carlo simulations.<\/jats:p>","DOI":"10.1093\/ectj\/utab013","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T10:56:18Z","timestamp":1619175378000},"page":"589-607","source":"Crossref","is-referenced-by-count":7,"title":["Exact computation of maximum rank correlation estimator"],"prefix":"10.1093","volume":"24","author":[{"given":"Youngki","family":"Shin","sequence":"first","affiliation":[{"name":"Department of Economics, McMaster University, 1280 Main Street W, Hamilton, ON L8S 4L8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zvezdomir","family":"Todorov","sequence":"additional","affiliation":[{"name":"Department of Economics, McMaster University, 1280 Main Street W, Hamilton, ON L8S 4L8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"issue":"3","key":"2021091009371864100_bib1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/S0165-1765(98)00255-9","article-title":"Computation of the maximum rank correlation estimator","volume":"62","author":"Abrevaya","year":"1999","journal-title":"Economics Letters"},{"issue":"1","key":"2021091009371864100_bib2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0304-4076(99)00027-5","article-title":"Rank estimation of a generalized fixed-effects regression model","volume":"95","author":"Abrevaya","year":"2000","journal-title":"Journal of Econometrics"},{"issue":"3","key":"2021091009371864100_bib3","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1198\/073500103288619070","article-title":"Pairwise-difference rank estimation of the transformation model","volume":"21","author":"Abrevaya","year":"2003","journal-title":"Journal of Business & Economic Statistics"},{"issue":"3","key":"2021091009371864100_bib4","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1111\/j.1368-423X.2011.00352.x","article-title":"Rank estimation of partially linear index models","volume":"14","author":"Abrevaya","year":"2011","journal-title":"The Econometrics Journal"},{"issue":"1","key":"2021091009371864100_bib5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07350015.2017.1379405","article-title":"Simple estimators for invertible index models","volume":"36","author":"Ahn","year":"2018","journal-title":"Journal of Business & Economic Statistics"},{"issue":"2","key":"2021091009371864100_bib6","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1214\/15-AOS1388","article-title":"Best subset selection via a modern optimization lens","volume":"44","author":"Bertsimas","year":"2016","journal-title":"The Annals of Statistics"},{"issue":"2","key":"2021091009371864100_bib7","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0304-4076(97)00090-0","article-title":"Rank estimators for monotonic index models","volume":"84","author":"Cavanagh","year":"1998","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2021091009371864100_bib8","doi-asserted-by":"crossref","first-page":"4","DOI":"10.2307\/146313","article-title":"Estimation of semiparametric censored regression models: an application to changes in black-white earnings inequality during the 1960s","volume":"33","author":"Chay","year":"1998","journal-title":"Journal of Human Resources"},{"issue":"1","key":"2021091009371864100_bib9","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jeconom.2018.05.001","article-title":"Best subset binary prediction","volume":"206","author":"Chen","year":"2018","journal-title":"Journal of Econometrics"},{"issue":"4","key":"2021091009371864100_bib10","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/jae.2619","article-title":"Exact computation of gmm estimators for instrumental variable quantile regression models","volume":"33","author":"Chen","year":"2018","journal-title":"Journal of Applied Econometrics"},{"issue":"4","key":"2021091009371864100_bib11","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1111\/1468-0262.00347","article-title":"Rank estimation of transformation models","volume":"70","author":"Chen","year":"2002","journal-title":"Econometrica"},{"issue":"2","key":"2021091009371864100_bib12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0304-4076(03)00100-3","article-title":"An mcmc approach to classical estimation","volume":"115","author":"Chernozhukov","year":"2003","journal-title":"Journal of Econometrics"},{"issue":"2","key":"2021091009371864100_bib13","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.jeconom.2019.08.003","article-title":"On rank estimators in increasing dimensions","volume":"214","author":"Fan","year":"2020","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2021091009371864100_bib14","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jeconom.2008.05.018","article-title":"Exact computation of max weighted score estimators","volume":"146","author":"Florios","year":"2008","journal-title":"Journal of Econometrics"},{"issue":"2\u20133","key":"2021091009371864100_bib15","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","article-title":"Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator","volume":"35","author":"Han","year":"1987","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2021091009371864100_bib16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0304-3975(78)90006-3","article-title":"The densest hemisphere problem","volume":"6","author":"Johnson","year":"1978","journal-title":"Theoretical Computer Science"},{"issue":"2","key":"2021091009371864100_bib17","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/S0304-4076(00)00040-3","article-title":"Two-stage rank estimation of quantile index models","volume":"100","author":"Khan","year":"2001","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2021091009371864100_bib19","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.jeconom.2006.03.003","article-title":"Partial rank estimation of duration models with general forms of censoring","volume":"136","author":"Khan","year":"2007","journal-title":"Journal of Econometrics"},{"issue":"2","key":"2021091009371864100_bib20","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.jeconom.2009.01.006","article-title":"Inference on endogenously censored regression models using conditional moment inequalities","volume":"152","author":"Khan","year":"2009","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2021091009371864100_bib21","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1080\/07350015.2017.1392312","article-title":"Discussion of 'simple estimators for invertible index models' by H. Ahn, H. Ichimura, J. Powell, and P. Ruud","volume":"36","author":"Khan","year":"2018","journal-title":"Journal of Business & Economic Statistics"},{"key":"2021091009371864100_bib18","article-title":"Inference onS emiparametric Multinomial Response Models","author":"Khan","year":"2020"},{"issue":"2","key":"2021091009371864100_bib22","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3982\/ECTA13288","article-title":"Who should be treated? Empirical welfare maximization methods for treatment choice","volume":"86","author":"Kitagawa","year":"2018","journal-title":"Econometrica"},{"key":"2021091009371864100_bib23","volume-title":"Introduction to Empirical Processes and Semiparametric Inference","author":"Kosorok","year":"2007"},{"key":"2021091009371864100_bib24","doi-asserted-by":"crossref","DOI":"10.1214\/20-AOS2017","article-title":"Factor-driven two-regime regression","volume-title":"The Annals of Statistics","author":"Lee","year":""},{"key":"2021091009371864100_bib25","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1214\/154957805100000186","article-title":"Tail behaviour of multiple random integrals and U-statistics","volume":"2","author":"Major","year":"2005","journal-title":"Probability Surveys"},{"issue":"3","key":"2021091009371864100_bib26","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0304-4076(75)90032-9","article-title":"Maximum score estimation of the stochastic utility model of choice","volume":"3","author":"Manski","year":"1975","journal-title":"Journal of Econometrics"},{"issue":"4","key":"2021091009371864100_bib27","doi-asserted-by":"crossref","first-page":"765","DOI":"10.2307\/1911029","article-title":"The sensitivity of an empirical model of married women\u2019s hours of work to economic and statistical assumptions","volume":"55","author":"Mroz","year":"1987","journal-title":"Econometrica"},{"issue":"2","key":"2021091009371864100_bib28","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1214\/aos\/1176350374","article-title":"U-processes: rates of convergence","volume":"15","author":"Nolan","year":"1987","journal-title":"The Annals of Statistics"},{"issue":"1","key":"2021091009371864100_bib29","doi-asserted-by":"crossref","first-page":"123","DOI":"10.2307\/2951780","article-title":"The limiting distribution of the maximum rank correlation estimator","volume":"61","author":"Sherman","year":"1993","journal-title":"Econometrica"},{"issue":"6","key":"2021091009371864100_bib30","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1017\/S026646660999079X","article-title":"Local rank estimation of transformation models with functional coefficients","volume":"26","author":"Shin","year":"2010","journal-title":"Econometric Theory"},{"issue":"1","key":"2021091009371864100_bib31","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1214\/aop\/1176988847","article-title":"Sharper bounds for Gaussian and empirical processes","volume":"22","author":"Talagrand","year":"1994","journal-title":"The Annals of Probability"},{"issue":"6","key":"2021091009371864100_bib32","doi-asserted-by":"crossref","first-page":"2803","DOI":"10.1016\/j.csda.2006.10.004","article-title":"A note on iterative marginal optimization: a simple algorithm for maximum rank correlation estimation","volume":"51","author":"Wang","year":"2007","journal-title":"Computational Statistics & Data Analysis"},{"key":"2021091009371864100_bib33","volume-title":"Integer Programming.","author":"Wolsey","year":"1998"}],"container-title":["The Econometrics Journal"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/ectj\/advance-article-pdf\/doi\/10.1093\/ectj\/utab013\/38338009\/utab013.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/ectj\/article-pdf\/24\/3\/589\/40344688\/utab013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/ectj\/article-pdf\/24\/3\/589\/40344688\/utab013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,25]],"date-time":"2022-12-25T08:40:42Z","timestamp":1671957642000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/ectj\/article\/24\/3\/589\/6247621"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,4,23]]},"published-print":{"date-parts":[[2021,9,10]]}},"URL":"https:\/\/doi.org\/10.1093\/ectj\/utab013","relation":{},"ISSN":["1368-4221","1368-423X"],"issn-type":[{"value":"1368-4221","type":"print"},{"value":"1368-423X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,9]]},"published":{"date-parts":[[2021,4,23]]}}}