{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T21:46:51Z","timestamp":1780350411042,"version":"3.54.1"},"reference-count":40,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T00:00:00Z","timestamp":1545091200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p>We propose a test for a generalized regression monotonicity (GRM) hypothesis. The GRM hypothesis is the sharp testable implication of the monotonicity of certain latent structures, as we show in this article. Examples include the monotonicity of the conditional mean function when only interval data are available for the dependent variable and the monotone instrumental variable assumption of Manski and Pepper (2000). These instances of latent monotonicity can be tested using our test. Moreover, the GRM hypothesis includes regression monotonicity and stochastic monotonicity as special cases. Thus, our test also serves as an alternative to existing tests for those hypotheses. We show that our test controls the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives, and has nontrivial power against some<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466618000439_inline1\"\/><jats:tex-math>${n^{ - 1\/2}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>local alternatives.<\/jats:p>","DOI":"10.1017\/s0266466618000439","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T09:24:56Z","timestamp":1545125096000},"page":"1146-1200","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":19,"title":["TESTING GENERALIZED REGRESSION MONOTONICITY"],"prefix":"10.1017","volume":"35","author":[{"given":"Yu-Chin","family":"Hsu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chu-An","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoxia","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,12,18]]},"reference":[{"key":"S0266466618000439_ref39","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.10094"},{"key":"S0266466618000439_ref38","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2545-2"},{"key":"S0266466618000439_ref35","unstructured":"Seo J . (2015) Tests of Stochastic Monotonicity with Improved Size and Power Properties, Working paper."},{"key":"S0266466618000439_ref34","doi-asserted-by":"crossref","DOI":"10.1214\/cbms\/1462061091","volume-title":"Empirical Processes: Theory and Application","volume":"2","author":"Pollard","year":"1990"},{"key":"S0266466618000439_ref33","doi-asserted-by":"publisher","DOI":"10.1177\/1536867X1501500205"},{"key":"S0266466618000439_ref32","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00294"},{"key":"S0266466618000439_ref31","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00262.x"},{"key":"S0266466618000439_ref30","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00144"},{"key":"S0266466618000439_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.08.006"},{"key":"S0266466618000439_ref26","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000997"},{"key":"S0266466618000439_ref25","doi-asserted-by":"publisher","DOI":"10.1353\/jhr.2009.0012"},{"key":"S0266466618000439_ref22","doi-asserted-by":"publisher","DOI":"10.1111\/ectj.12077"},{"key":"S0266466618000439_ref21","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1214\/aos\/1016120363","article-title":"Testing for monotonicity of a regression mean by calibrating for linear functions","volume":"28","author":"Hall","year":"2000","journal-title":"Annals of Statistics"},{"key":"S0266466618000439_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.06.007"},{"key":"S0266466618000439_ref18","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1214\/aos\/1015956707","article-title":"Testing monotonicity of regression","volume":"28","author":"Ghosal","year":"2000","journal-title":"Annals of Statistics"},{"key":"S0266466618000439_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(03)00122-6"},{"key":"S0266466618000439_ref15","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2013.833813"},{"key":"S0266466618000439_ref24","volume-title":"Elements of the Theory of Functions and Functional Analysis, Volume 1: Metric and Normed Spaces","author":"Kolmogorov","year":"1957"},{"key":"S0266466618000439_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.02.005"},{"key":"S0266466618000439_ref13","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13639"},{"key":"S0266466618000439_ref12","doi-asserted-by":"publisher","DOI":"10.1920\/wp.cem.2012.3512"},{"key":"S0266466618000439_ref10","unstructured":"Chernozhukov V. , Chetverikov D. , & Kato K. (2015a) Comparison and anti-concentration Bounds for Maxima of Gaussian Random Vectors"},{"key":"S0266466618000439_ref23","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA11974"},{"key":"S0266466618000439_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1235"},{"key":"S0266466618000439_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000896"},{"key":"S0266466618000439_ref2","first-page":"1","article-title":"Supplement to \u2018Inference based on conditional moment inequalities\u2019","volume":"81","author":"Andrews","year":"2013b","journal-title":"Econometrica Supplemental Material"},{"key":"S0266466618000439_ref1","doi-asserted-by":"crossref","first-page":"609","DOI":"10.3982\/ECTA9370","article-title":"Inference based on conditional moment inequalities","volume":"81","author":"Andrews","year":"2013a","journal-title":"Econometrica"},{"key":"S0266466618000439_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466617000329"},{"key":"S0266466618000439_ref7","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/10618600.1998.10474790","article-title":"Testing monotonicity of regression","volume":"7","author":"Bowman","year":"1998","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"S0266466618000439_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.10.005"},{"key":"S0266466618000439_ref37","first-page":"110","volume-title":"Nonparametric Statistical Inference","volume":"2","author":"Schlee","year":"1982"},{"key":"S0266466618000439_ref36","volume-title":"Journal of Business and Economic Statistics","author":"Shen","year":"2016"},{"key":"S0266466618000439_ref40","doi-asserted-by":"publisher","DOI":"10.2307\/2938170"},{"key":"S0266466618000439_ref11","doi-asserted-by":"publisher","DOI":"10.1920\/wp.cem.2016.4216"},{"key":"S0266466618000439_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139052276.004"},{"key":"S0266466618000439_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/996986504"},{"key":"S0266466618000439_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2016.09.010"},{"key":"S0266466618000439_ref27","doi-asserted-by":"crossref","first-page":"585","DOI":"10.3982\/ECTA7145","article-title":"Testing for stochastic monotonicity","volume":"77","author":"Lee","year":"2009","journal-title":"Econometrica"},{"key":"S0266466618000439_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.10.013"},{"key":"S0266466618000439_ref19","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/87.3.663"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466618000439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T12:27:01Z","timestamp":1720873621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466618000439\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,18]]},"references-count":40,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["S0266466618000439"],"URL":"https:\/\/doi.org\/10.1017\/s0266466618000439","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,18]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2018\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}