{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T07:34:54Z","timestamp":1791617694864,"version":"4.3.4"},"reference-count":85,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":505,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000105","name":"OAC","doi-asserted-by":"publisher","award":["1934578"],"award-info":[{"award-number":["1934578"]}],"id":[{"id":"10.13039\/100000105","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-20-12157"],"award-info":[{"award-number":["N00014-20-12157"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these methods enjoy some theoretical appeal in terms of consistency and convergence rates, they generally perform poorly in terms of uncertainty quantification. This is troubling since assessing risk is crucial for reliable decision-making in sensitive and uncertain environments. In this work, we propose a conformal inference-based approach that can produce reliable interval estimates for counterfactuals and individual treatment effects under the potential outcome framework. For completely randomized or stratified randomized experiments with perfect compliance, the intervals have guaranteed average coverage in finite samples regardless of the unknown data generating mechanism. For randomized experiments with ignorable compliance and general observational studies obeying the strong ignorability assumption, the intervals satisfy a doubly robust property which states the following: the average coverage is approximately controlled if either the propensity score or the conditional quantiles of potential outcomes can be estimated accurately. Numerical studies on both synthetic and real data sets empirically demonstrate that existing methods suffer from a significant coverage deficit even in simple models. In contrast, our methods achieve the desired coverage with reasonably short intervals.<\/jats:p>","DOI":"10.1111\/rssb.12445","type":"journal-article","created":{"date-parts":[[2021,10,9]],"date-time":"2021-10-09T11:02:12Z","timestamp":1633777332000},"page":"911-938","source":"Crossref","is-referenced-by-count":99,"title":["Conformal Inference of Counterfactuals and Individual Treatment Effects"],"prefix":"10.1093","volume":"83","author":[{"given":"Lihua","family":"Lei","sequence":"first","affiliation":[{"name":"Department of Statistics , , Stanford, California , USA"},{"name":"Stanford University , , Stanford, California , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuel J.","family":"Cand\u00e8s","sequence":"additional","affiliation":[{"name":"Department of Statistics , , Stanford, California , USA"},{"name":"Stanford University , , Stanford, California , USA"},{"name":"Department of Mathematics , , Stanford, California , USA"},{"name":"Stanford University , , Stanford, California , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,10,7]]},"reference":[{"key":"2023022501101278300_","article-title":"Synthetic difference in differences","author":"Arkhangelsky","year":"2018"},{"key":"2023022501101278300_","article-title":"Matrix completion methods for causal panel data models","author":"Athey","year":"2017"},{"issue":"2","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1214\/18-AOS1709","article-title":"Generalized random forests","volume":"47","author":"Athey","year":"2019","journal-title":"The Annals of Statistics"},{"key":"2023022501101278300_","volume-title":"Conformal prediction for reliable machine learning: theory, adaptations and applications","author":"Balasubramanian","year":"2014"},{"key":"2023022501101278300_","article-title":"The limits of distribution-free conditional predictive inference","volume-title":"arXiv preprint","author":"Barber","year":"2019"},{"key":"2023022501101278300_","article-title":"Predictive inference with the jackknife+","volume-title":"arXiv preprint","author":"Barber","year":"2019"},{"key":"2023022501101278300_","article-title":"The augmented synthetic control method","volume-title":"arXiv preprint","author":"Ben-Michael","year":"2018"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1037\/xge0000558","article-title":"Causal processes in psychology are heterogeneous","volume":"148","author":"Bolger","year":"2019","journal-title":"Journal of Experimental Psychology: General"},{"issue":"2","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1177\/0003122410363567","article-title":"Who benefits most from college? Evidence for negative selection in heterogeneous economic returns to higher education","volume":"75","author":"Brand","year":"2010","journal-title":"American Sociological Review"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"351","DOI":"10.15195\/v2.a17","article-title":"Heterogeneous causal effects and sample selection bias","volume":"2","author":"Breen","year":"2015","journal-title":"Sociological Science"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","DOI":"10.1353\/obs.2019.0000","article-title":"Assessing treatment effect variation in observational studies: results from a data challenge","volume-title":"arXiv preprint","author":"Carvalho","year":"2019"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1214\/09-AOAS285","article-title":"BART: Bayesian additive regression trees","volume":"4","author":"Chipman","year":"2010","journal-title":"The Annals of Applied Statistics"},{"key":"2023022501101278300_","article-title":"Overlap in observational studies with high-dimensional covariates","volume-title":"arXiv preprint","author":"D\u2019Amour","year":"2017"},{"issue":"1\u20132","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.jeconom.2008.05.012","article-title":"Heterogeneous impacts in PROGRESA","volume":"145","author":"Djebbari","year":"2008","journal-title":"Journal of Econometrics"},{"key":"2023022501101278300_","first-page":"2017","article-title":"aciccomp2016: Atlantic causal inference conference competition 2016 simulation","volume":"1\u20130","author":"Dorie","year":"2017","journal-title":"R package version"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1214\/18-STS667","article-title":"Automated versus do-it-yourself methods for causal inference: lessons learned from a data analysis competition","volume":"34","author":"Dorie","year":"2019","journal-title":"Statistical Science"},{"issue":"507","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1080\/01621459.2013.823775","article-title":"Estimation and accuracy after model selection","volume":"109","author":"Efron","year":"2014","journal-title":"Journal of the American Statistical Association"},{"issue":"5","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.3982\/ECTA5317","article-title":"Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects","volume":"76","author":"Florens","year":"2008","journal-title":"Econometrica"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/978-3-319-27274-0_2","volume-title":"Topics in theoretical and applied statistics","author":"Fort","year":"2016"},{"key":"2023022501101278300_","article-title":"Orthogonal statistical learning","volume-title":"arXiv preprint","author":"Foster","year":"2019"},{"key":"2023022501101278300_","first-page":"1189","article-title":"Greedy function approximation: a gradient boosting machine","author":"Friedman","year":"2001","journal-title":"Annals of Statistics"},{"issue":"2","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1093\/comjnl\/bxl065","article-title":"Hedging predictions in machine learning","volume":"50","author":"Gammerman","year":"2007","journal-title":"The Computer Journal"},{"key":"2023022501101278300_","volume-title":"Discovering causal structure: artificial intelligence, philosophy of science, and statistical modeling","author":"Glymour","year":"2014"},{"issue":"3","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1093\/poq\/nfs036","article-title":"Modeling heterogeneous treatment effects in survey experiments with bayesian additive regression trees","volume":"76","author":"Green","year":"2012","journal-title":"Public Opinion Quarterly"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1097\/00001648-199901000-00008","article-title":"Causal diagrams for epidemiologic research","volume":"10","author":"Greenland","year":"1999","journal-title":"Epidemiology"},{"issue":"1","key":"2023022501101278300_","first-page":"5","article-title":"gbm: generalized boosted regression models","volume":"2","author":"Greenwell","year":"2019","journal-title":"R package version"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1017\/pan.2017.15","article-title":"Estimating heterogeneous treatment effects and the effects of heterogeneous treatments with ensemble methods","volume":"25","author":"Grimmer","year":"2017","journal-title":"Political Analysis"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1214\/19-BA1195","article-title":"Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects","volume":"15","author":"Hahn","year":"2020","journal-title":"Bayesian Analysis"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1198\/jcgs.2010.08162","article-title":"Bayesian nonparametric modeling for causal inference","volume":"20","author":"Hill","year":"2011","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1111\/1468-0262.00442","article-title":"Efficient estimation of average treatment effects using the estimated propensity score","volume":"71","author":"Hirano","year":"2003","journal-title":"Econometrica"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/pan\/mpq035","article-title":"Estimation of heterogeneous treatment effects from randomized experiments, with application to the optimal planning of the get-out-the-vote campaign","volume":"19","author":"Imai","year":"2011","journal-title":"Political Analysis"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal inference in statistics, social, and biomedical sciences","author":"Imbens","year":"2015"},{"issue":"4","key":"2023022501101278300_","first-page":"523","article-title":"Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data","volume":"22","author":"Kang","year":"2007","journal-title":"Statistical Science"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v070.i04","article-title":"bartMachine: machine learning with Bayesian additive regression trees","volume":"70","author":"Kapelner","year":"2016","journal-title":"Journal of Statistical Software"},{"key":"2023022501101278300_","article-title":"Optimal doubly robust estimation of heterogeneous causal effects","volume-title":"arXiv preprint","author":"Kennedy","year":"2020"},{"key":"2023022501101278300_","article-title":"Conformal prediction intervals for the individual treatment effect","volume-title":"arXiv preprint","author":"Kivaranovic","year":"2020"},{"key":"2023022501101278300_","first-page":"349","volume-title":"Confidence intervals for regression quantiles","author":"Koenker","year":"1994"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511754098","volume-title":"Quantile regression","author":"Koenker","year":"2005"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1146\/annurev-economics-063016-103651","article-title":"Quantile regression: 40 years on","volume":"9","author":"Koenker","year":"2017","journal-title":"Annual Review of Economics"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/1913643","article-title":"Regression quantiles","volume":"46","author":"Koenker","year":"1978","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1257\/jep.15.4.143","article-title":"Quantile regression","volume":"15","author":"Koenker","year":"2001","journal-title":"Journal of Economic Perspectives"},{"issue":"10","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"4156","DOI":"10.1073\/pnas.1804597116","article-title":"Metalearners for estimating heterogeneous treatment effects using machine learning","volume":"116","author":"K\u00fcnzel","year":"2019","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2023022501101278300_","article-title":"causalToolbox: toolbox for causal inference with emphasize on heterogeneous treatment effect estimator","author":"K\u00fcnzel","year":"2020"},{"issue":"523","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1080\/01621459.2017.1307116","article-title":"Distribution-free predictive inference for regression","volume":"113","author":"Lei","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"501","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1080\/01621459.2012.751873","article-title":"Distribution-free prediction sets","volume":"108","author":"Lei","year":"2013","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1111\/rssb.12021","article-title":"Distribution-free prediction bands for non-parametric regression","volume":"76","author":"Lei","year":"2014","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"6","key":"2023022501101278300_","article-title":"Quantile regression forests","volume":"7","author":"Meinshausen","year":"2006","journal-title":"Journal of Machine Learning Research"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/2673139","article-title":"Counterfactuals, causal effect heterogeneity, and the catholic school effect on learning","volume":"74","author":"Morgan","year":"2001","journal-title":"Sociology of Education"},{"key":"2023022501101278300_","first-page":"465","article-title":"On the application of probability theory to agricultural experiments. Essay on principles. Section 9","volume":"5","author":"Neyman","year":"1923\/1990","journal-title":"Statistical Science"},{"key":"2023022501101278300_","article-title":"Quasi-oracle estimation of heterogeneous treatment effects","volume-title":"arXiv preprint","author":"Nie","year":"2017"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1093\/biomet\/82.4.669","article-title":"Causal diagrams for empirical research","volume":"82","author":"Pearl","year":"1995","journal-title":"Biometrika"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1214\/14-STS486","article-title":"External validity: from do-calculus to transportability across populations","volume":"29","author":"Pearl","year":"2014","journal-title":"Statistical Science"},{"key":"2023022501101278300_","volume-title":"Causal inference in statistics: a primer","author":"Pearl","year":"2016"},{"key":"2023022501101278300_","volume-title":"The book of why: the new science of cause and effect","author":"Pearl","year":"2018"},{"issue":"5","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1111\/rssb.12167","article-title":"Causal inference by using invariant prediction: identification and confidence intervals","volume":"78","author":"Peters","year":"2016","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"30","key":"2023022501101278300_","article-title":"Single world intervention graphs (SWIGS): a unification of the counterfactual and graphical approaches to causality. Center for the Statistics and the Social Sciences, University of Washington Series","volume":"128","author":"Richardson","year":"2013","journal-title":"Working Paper"},{"issue":"427","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/01621459.1994.10476818","article-title":"Estimation of regression coefficients when some regressors are not always observed","volume":"89","author":"Robins","year":"1994","journal-title":"Journal of the American statistical Association"},{"key":"2023022501101278300_","first-page":"3538","article-title":"Conformalized quantile regression","author":"Romano","year":"2019","journal-title":"In Advances in neural information processing systems"},{"key":"2023022501101278300_","article-title":"Classification with valid and adaptive coverage","volume-title":"arXiv preprint","author":"Romano","year":"2020"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","article-title":"The central role of the propensity score in observational studies for causal effects","volume":"70","author":"Rosenbaum","year":"1983","journal-title":"Biometrika"},{"issue":"5","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1037\/h0037350","article-title":"Estimating causal effects of treatments in randomized and nonrandomized studies","volume":"66","author":"Rubin","year":"1974","journal-title":"Journal of Educational Psychology"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1214\/aos\/1176344064","article-title":"Bayesian inference for causal effects: The role of randomization","volume":"6","author":"Rubin","year":"1978","journal-title":"The Annals of Statistics"},{"issue":"3","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0378-3758(90)90077-8","article-title":"Formal mode of statistical inference for causal effects","volume":"25","author":"Rubin","year":"1990","journal-title":"Journal of Statistical Planning and Inference"},{"issue":"525","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/01621459.2017.1395341","article-title":"Least ambiguous set-valued classifiers with bounded error levels","volume":"114","author":"Sadinle","year":"2019","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"e261","DOI":"10.1002\/sta4.261","article-title":"A comparison of some conformal quantile regression methods","volume":"9","author":"Sesia","year":"2020","journal-title":"Stat"},{"key":"2023022501101278300_","first-page":"371","article-title":"A tutorial on conformal prediction","volume":"9","author":"Shafer","year":"2008","journal-title":"Journal of Machine Learning Research"},{"issue":"2","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0378-3758(00)00115-4","article-title":"Improving predictive inference under covariate shift by weighting the log-likelihood function","volume":"90","author":"Shimodaira","year":"2000","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2023022501101278300_","volume-title":"Causation, prediction, and search","author":"Spirtes","year":"2000"},{"issue":"2","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1111\/j.1467-985X.2010.00673.x","article-title":"The use of propensity scores to assess the generalizability of results from randomized trials","volume":"174","author":"Stuart","year":"2011","journal-title":"Journal of the Royal Statistical Society: Series A (Statistics in Society)"},{"key":"2023022501101278300_","doi-asserted-by":"crossref","DOI":"10.1101\/2019.12.20.19015511","article-title":"Use of directed acyclic graphs (DAGS) in applied health research: review and recommendations","volume-title":"medRxiv","author":"Tennant","year":"2019"},{"key":"2023022501101278300_","first-page":"1","article-title":"grf: generalized random forests","volume":"1","author":"Tibshirani","year":"2019","journal-title":"R package version"},{"key":"2023022501101278300_","first-page":"2530","article-title":"Conformal prediction under covariate shift","author":"Tibshirani","year":"2019","journal-title":"Advances in neural information processing systems"},{"issue":"3","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"239","DOI":"10.3102\/1076998612441947","article-title":"Improving generalizations from experiments using propensity score subclassification: Assumptions, properties, and contexts","volume":"38","author":"Tipton","year":"2013","journal-title":"Journal of Educational and Behavioral Statistics"},{"issue":"6","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"478","DOI":"10.3102\/1076998614558486","article-title":"How generalizable is your experiment? An index for comparing experimental samples and populations","volume":"39","author":"Tipton","year":"2014","journal-title":"Journal of Educational and Behavioral Statistics"},{"key":"2023022501101278300_","first-page":"475","article-title":"Asian conference on machine learning","author":"Vovk","year":"2012","journal-title":"Conditional validity of inductive conformal predictors"},{"key":"2023022501101278300_","first-page":"348","article-title":"IFIP international conference on artificial intelligence applications and innovations","author":"Vovk","year":"2013","journal-title":"Transductive conformal predictors Springer"},{"issue":"1\u20132","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s10472-013-9368-4","article-title":"Cross-conformal predictors","volume":"74","author":"Vovk","year":"2015","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"2023022501101278300_","volume-title":"Algorithmic learning in a random world","author":"Vovk","year":"2005"},{"issue":"3","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1214\/08-AOS622","article-title":"On-line predictive linear regression","volume":"37","author":"Vovk","year":"2009","journal-title":"The Annals of Statistics"},{"issue":"523","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1080\/01621459.2017.1319839","article-title":"Estimation and inference of heterogeneous treatment effects using random forests","volume":"113","author":"Wager","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023022501101278300_","first-page":"1625","article-title":"Confidence intervals for random forests: The jackknife and the infinitesimal jackknife","volume":"15","author":"Wager","year":"2014","journal-title":"The Journal of Machine Learning Research"},{"issue":"10","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1001\/jamapsychiatry.2019.1530","article-title":"Evaluation of differences in individual treatment response in schizophrenia spectrum disorders: a meta-analysis","volume":"76","author":"Winkelbeiner","year":"2019","journal-title":"JAMA Psychiatry"},{"issue":"1","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1177\/0081175012452652","article-title":"Estimating heterogeneous treatment effects with observational data","volume":"42","author":"Xie","year":"2012","journal-title":"Sociological Methodology"},{"issue":"7774","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1038\/s41586-019-1466-y","article-title":"A national experiment reveals where a growth mindset improves achievement","volume":"573","author":"Yeager","year":"2019","journal-title":"Nature"},{"issue":"4","key":"2023022501101278300_","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/S0167-7152(01)00124-9","article-title":"Bayesian quantile regression","volume":"54","author":"Yu","year":"2001","journal-title":"Statistics & Probability Letters"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12445","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12445","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/rssb.12445","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/83\/5\/911\/49322261\/jrsssb_83_5_911.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/83\/5\/911\/49322261\/jrsssb_83_5_911.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T12:28:51Z","timestamp":1699619331000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/83\/5\/911\/7056131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,7]]},"references-count":85,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,10,7]]},"published-print":{"date-parts":[[2021,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12445","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,11]]},"published":{"date-parts":[[2021,10,7]]}}}