{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T16:53:19Z","timestamp":1791219199323,"version":"4.1.0"},"reference-count":43,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>\n                    We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we use critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean\u2010squared error results in CIs that are nearly efficient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\u22122\/5<\/jats:sup>\n                    , the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in a Monte Carlo analysis and an empirical application.\n                  <\/jats:p>","DOI":"10.3982\/qe1199","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:51:29Z","timestamp":1580111489000},"page":"1-39","source":"Crossref","is-referenced-by-count":76,"title":["Simple and honest confidence intervals in nonparametric regression"],"prefix":"10.3982","volume":"11","author":[{"given":"Timothy B.","family":"Armstrong","sequence":"first","affiliation":[{"name":"Department of Economics, Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michal","family":"Koles\u00e1r","sequence":"additional","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"issue":"1","key":"quan200073-bib-0001","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1111\/j.1468-0262.2006.00655.x","volume":"74","author":"Abadie","year":"2006","journal-title":"Econometrica"},{"issue":"508","key":"quan200073-bib-0002","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1080\/01621459.2014.928218","volume":"109","author":"Abadie","year":"2014","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"quan200073-bib-0003","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1214\/aoms\/1177730090","volume":"20","author":"Anderson","year":"1949","journal-title":"The Annals of Mathematical Statistics"},{"key":"quan200073-bib-0004","doi-asserted-by":"crossref","unstructured":"Armstrong, T. B., and M. Koles\u00e1r (2020), \u201cSupplement to \u2018Simple and honest confidence intervals in nonparametric regression\u2019.\u201d Quantitative Economics Supplemental Material, 11, https:\/\/doi.org\/10.3982\/QE1199.","DOI":"10.3982\/QE1199"},{"key":"quan200073-bib-0005","doi-asserted-by":"crossref","unstructured":"Armstrong, T. B. (2019), \u201cAdaptation bounds for confidence bands under self-similarity.\u201d Available at arXiv:1810.09762.","DOI":"10.2139\/ssrn.3423277"},{"issue":"2","key":"quan200073-bib-0006","doi-asserted-by":"crossref","first-page":"655","DOI":"10.3982\/ECTA14434","volume":"86","author":"Armstrong","year":"2018","journal-title":"Econometrica"},{"issue":"2","key":"quan200073-bib-0007","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1093\/restud\/rdx051","volume":"85","author":"Armstrong","year":"2018","journal-title":"Review of Economic Studies"},{"issue":"6","key":"quan200073-bib-0008","doi-asserted-by":"crossref","first-page":"2384","DOI":"10.1214\/aos\/1032181159","volume":"24","author":"Brown","year":"1996","journal-title":"The Annals of Statistics"},{"issue":"6","key":"quan200073-bib-0009","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1214\/aos\/1030741087","volume":"25","author":"Brown","year":"1997","journal-title":"The Annals of Statistics"},{"key":"quan200073-bib-0010","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1214\/12-EJS720","volume":"6","author":"Bull","year":"2012","journal-title":"Electronic Journal of Statistics"},{"issue":"5","key":"quan200073-bib-0011","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1214\/009053604000000049","volume":"32","author":"Cai","year":"2004","journal-title":"The Annals of Statistics"},{"issue":"522","key":"quan200073-bib-0012","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1080\/01621459.2017.1285776","volume":"113","author":"Calonico","year":"2018","journal-title":"Journal of the American Statistical Association"},{"key":"quan200073-bib-0013","unstructured":"Calonico, S., M. D. Cattaneo, and M. H. Farrell (2019), \u201cCoverage error optimal confidence intervals for local polynomial regression.\u201d Available at arXiv:1808.01398."},{"issue":"6","key":"quan200073-bib-0014","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.3982\/ECTA11757","volume":"82","author":"Calonico","year":"2014","journal-title":"Econometrica"},{"issue":"4","key":"quan200073-bib-0015","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1214\/aos\/1031594737","volume":"25","author":"Cheng","year":"1997","journal-title":"The Annals of Statistics"},{"issue":"5","key":"quan200073-bib-0016","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1214\/14-AOS1235","volume":"42","author":"Chernozhukov","year":"2014","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0017","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1214\/aos\/1176325367","volume":"22","author":"Donoho","year":"1994","journal-title":"The Annals of Statistics"},{"issue":"2","key":"quan200073-bib-0018","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1214\/aos\/1176348665","volume":"20","author":"Donoho","year":"1992","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0019","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1214\/aos\/1176349022","volume":"21","author":"Fan","year":"1993","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0020","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1023\/A:1003162622169","volume":"49","author":"Fan","year":"1997","journal-title":"Annals of the Institute of Statistical Mathematics"},{"key":"quan200073-bib-0021","series-title":"Monographs on Statistics and Applied Probability","volume-title":"Local Polynomial Modelling and Its Applications","author":"Fan","year":"1996"},{"key":"quan200073-bib-0022","first-page":"510","volume-title":"Automatic and Remote Control: Proceedings of the First International Congress of the International Federation of Automatic Control","volume":"1","author":"Fuller","year":"1961"},{"key":"quan200073-bib-0023","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.jmva.2018.01.001","volume":"165","author":"Gao","year":"2018","journal-title":"Journal of Multivariate Analysis"},{"issue":"2","key":"quan200073-bib-0024","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1214\/09-AOS738","volume":"38","author":"Gin\u00e9","year":"2010","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0025","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1111\/1468-0262.00183","volume":"69","author":"Hahn","year":"2001","journal-title":"Econometrica"},{"issue":"2","key":"quan200073-bib-0026","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1214\/aos\/1176348651","volume":"20","author":"Hall","year":"1992","journal-title":"The Annals of Statistics"},{"issue":"4","key":"quan200073-bib-0027","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1214\/13-AOS1137","volume":"41","author":"Hall","year":"2013","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0028","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1137\/1129002","volume":"29","author":"Ibragimov","year":"1985","journal-title":"Theory of Probability & Its Applications"},{"issue":"2","key":"quan200073-bib-0029","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1162\/rest_a_00793","volume":"101","author":"Imbens","year":"2019","journal-title":"Review of Economics and Statistics"},{"issue":"8","key":"quan200073-bib-0030","doi-asserted-by":"crossref","first-page":"2277","DOI":"10.1257\/aer.20160945","volume":"108","author":"Koles\u00e1r","year":"2018","journal-title":"American Economic Review"},{"issue":"2","key":"quan200073-bib-0031","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1137\/1116031","volume":"16","author":"Legostaeva","year":"1971","journal-title":"Theory of Probability & Its Applications"},{"issue":"3","key":"quan200073-bib-0032","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1137\/1135065","volume":"35","author":"Lepski","year":"1990","journal-title":"Theory of Probability & Its Applications"},{"issue":"3","key":"quan200073-bib-0033","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1214\/aos\/1176347253","volume":"17","author":"Li","year":"1989","journal-title":"The Annals of Statistics"},{"issue":"6","key":"quan200073-bib-0034","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1214\/aos\/1030741084","volume":"25","author":"Low","year":"1997","journal-title":"The Annals of Statistics"},{"issue":"1","key":"quan200073-bib-0035","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1162\/qjec.122.1.159","volume":"122","author":"Ludwig","year":"2007","journal-title":"Quarterly Journal of Economics"},{"key":"quan200073-bib-0036","unstructured":"Noack, C. and C. Rothe (2019), \u201cBias-aware inference in fuzzy regression discontinuity designs.\u201d Unpublished manuscript, University of Mannheim."},{"issue":"6","key":"quan200073-bib-0037","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1214\/aos\/1032181160","volume":"24","author":"Nussbaum","year":"1996","journal-title":"The Annals of Statistics"},{"issue":"5","key":"quan200073-bib-0038","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1214\/aos\/1176344315","volume":"6","author":"Sacks","year":"1978","journal-title":"The Annals of Statistics"},{"key":"quan200073-bib-0039","doi-asserted-by":"crossref","unstructured":"Schennach, S. M. (2015), \u201cA bias bound approach to nonparametric inference.\u201d Working Paper CWP71\/15, Cemmap.","DOI":"10.1920\/wp.cem.2015.7115"},{"key":"quan200073-bib-0040","doi-asserted-by":"crossref","unstructured":"Sun, Y. (2005), \u201cAdaptive estimation of the regression discontinuity model.\u201d Unpublished manuscript, Univesity of California, San Diego.","DOI":"10.2139\/ssrn.739151"},{"key":"quan200073-bib-0041","doi-asserted-by":"crossref","DOI":"10.1007\/b13794","volume-title":"Introduction to Nonparametric Estimation","author":"Tsybakov","year":"2009"},{"key":"quan200073-bib-0042","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","author":"Vaart","year":"1998"},{"issue":"2","key":"quan200073-bib-0043","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1214\/aos\/1031833671","volume":"25","author":"Zhao","year":"1997","journal-title":"The Annals of Statistics"}],"container-title":["Quantitative Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.3982\/QE1199","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:52:35Z","timestamp":1580111555000},"score":1,"resource":{"primary":{"URL":"http:\/\/qeconomics.org\/ojs\/index.php\/qe\/article\/view\/QE1199"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020]]}},"alternative-id":["10.3982\/QE1199"],"URL":"https:\/\/doi.org\/10.3982\/qe1199","relation":{},"ISSN":["1759-7323"],"issn-type":[{"value":"1759-7323","type":"print"}],"subject":[],"published":{"date-parts":[[2020]]}}}