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The procedure applies a two-step design: estimate the propensity score, then perform a blocking estimation using this estimate to compute treatment effects. The paper proves consistency of the proposed estimators, reports Monte Carlo evidence of improved performance versus other propensity-score-based methods, and demonstrates the approach on a job training dataset.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/nonparametric-estimation-of-ate-and-qte-an-application-of-fractile-graphical-analysis/201995/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/nonparametric-estimation-of-ate-and-qte-an-application-of-fractile-graphical-analysis/201995.png","ImageObject",300,407,{"name":92,"@type":93},"Theodore","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What identifying assumption is used for estimating ATE and QTE?","Question",{"text":113,"@type":114},"The method assumes selection to treatment is based on observable characteristics, so conditional on exogenous covariates treatment occurrence is statistically independent of potential outcomes.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the proposed two-step estimation procedure work?",{"text":118,"@type":114},"First, the propensity score is estimated; second, a blocking estimation procedure using this propensity score estimate is used to compute treatment effects.",{"name":120,"@type":111,"acceptedAnswer":121},"What evidence supports the effectiveness of the proposed estimators?",{"text":122,"@type":114},"Consistency is proved for the proposed estimators, and Monte Carlo results show better performance than other procedures based on the propensity score. 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Nonparametric estimation of ATE and QTE: An application of fractile graphical analysis. Journal of Probability and Statistics,  \n2011(1), pp. 1-23. doi: 10.1155/2011/874251 This is the accepted version of the paper.  \nThis version of the publication may differ from the final published version. To cite this item please consult the publisher's version.  \nPermanent repository link: [https://openaccess.city.ac.uk/id/eprint/12027/](https://openaccess.city.ac.uk/id/eprint/12027/)  \nLink to published version: [https://doi.org/10.1155/2011/874251](https://doi.org/10.1155/2011/874251)  \nCopyright and Reuse: Copyright and Moral Rights remain with the author(s) and/or copyright holders. Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge, unless otherwise indicated, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. For full details of reuse please refer to City Research Online policy.  \nCity Research Online:  [http://openaccess.city.ac.uk/](http://openaccess.city.ac.uk/  publications@citystgeorges.ac.uk)[ ](http://openaccess.city.ac.uk/  publications@citystgeorges.ac.uk)[ publications@citystgeorges.ac.uk](http://openaccess.city.ac.uk/  publications@citystgeorges.ac.uk)  \nHindawi Publishing Corporation Journal of Probability and Statistics Volume 2011, Article ID 874251, 23 pages doi:10.1155/2011/874251  \nResearch Article  \nNonparametric Estimation of ATE and QTE: An Application of Fractile Graphical Analysis  \nGabriel V. Montes-Rojas  \nDepartment of Economics, City University London, D306 Social Sciences Building, Northampton Square, London EC1V 0HB, UK  \nCorrespondence should be addressed to Gabriel V. Montes-Rojas, [gabriel.montes-rojas.1@city.ac.uk](gabriel.montes-rojas.1@city.ac.uk)[ ](gabriel.montes-rojas.1@city.ac.uk)Received 3 May 2011; Accepted 28 July 2011  \nAcademic Editor: Mike Tsionas  \nCopyright q 2011 Gabriel V. Montes-Rojas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.  \nNonparametric estimators for average and quantile treatment effects are constructed using Fractile Graphical Analysis, under the identifying assumption that selection to treatment is based on observable characteristics. The proposed method has two steps: first, the propensity score is estimated, and, second, a blocking estimation procedure using this estimate is used to compute treatment effects. In both cases, the estimators are proved to be consistent. Monte Carlo results show a better performance than other procedures based on the propensity score. Finally, these estimators are applied to a job training dataset.  \n1. Introduction  \nEconometric methods for estimating the effects of certain programs 􀀃such as job search assistance or classroom teaching programs􀀄 has been widely developed since the pioneering work of Ashenfelter 􀀅1􀀆, LaLonde 􀀅2􀀆, and others. In this case, a treatment refers to a certain program whose benefits are potentially obtainable by those selected for participation 􀀃treated􀀄, and it has no effect on a control group 􀀃nontreated􀀄 .  \nEstimating average treatment effects 􀀃ATEs􀀄, which refers to the mean effect of the program on a given outcome variable in parametric and nonparametric environments 􀀃 see 􀀅3, 4􀀆􀀄, has been a central issue in the literature. Lehmann 􀀅5􀀆 and Doksum 􀀅6􀀆 introduced the concept of quantile treatment effects 􀀃QTEs􀀄 as the difference of the quantiles of the treated and control outcome distributions. In this case, it is implicitly assumed that individuals have an intrinsic heterogeneity which cannot be controlled for using observables. Bitler","cbCaipVPmll4wCoW","https://ap.wps.com/l/cbCaipVPmll4wCoW","pdf",596680,24,"English","# Introduction\n## Background on ATE and QTE\n## Challenges in nonexperimental settings\n## Propensity score methods for ATE and QTE","[{\"question\":\"What identifying assumption is used for estimating ATE and QTE?\",\"answer\":\"The method assumes selection to treatment is based on observable characteristics, so conditional on exogenous covariates treatment occurrence is statistically independent of potential outcomes.\"},{\"question\":\"How does the proposed two-step estimation procedure work?\",\"answer\":\"First, the propensity score is estimated; second, a blocking estimation procedure using this propensity score estimate is used to compute treatment effects.\"},{\"question\":\"What evidence supports the effectiveness of the proposed estimators?\",\"answer\":\"Consistency is proved for the proposed estimators, and Monte Carlo results show better performance than other procedures based on the propensity score. The method is also applied to a job training dataset.\"}]","Nonparametric Estimation of ATE and QTE - An Application of Fractile Graphical Analysis | PDF"]