{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T18:28:12Z","timestamp":1774376892632,"version":"3.50.1"},"reference-count":52,"publisher":"The Econometric Society","issue":"5","funder":[{"DOI":"10.13039\/501100006447","name":"Universit\u00e4t Z\u00fcrich","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006447","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003006","name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>This paper analyzes a procedure called Testing\u2010Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for deciding which covariate to include next and when to stop including covariates is derived from a profile of traditional statistical hypothesis tests. This paper proves probabilistic bounds, which depend on the quality of the tests, for prediction error and the number of selected covariates. As an example, the bounds are then specialized to a case with heteroscedastic data, with tests constructed with the help of Huber\u2013Eicker\u2013White standard errors. Under the assumed regularity conditions, these tests lead to estimation convergence rates matching other common high\u2010dimensional estimators including Lasso.<\/jats:p>","DOI":"10.3982\/ecta16273","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T12:02:27Z","timestamp":1600689747000},"page":"2147-2173","source":"Crossref","is-referenced-by-count":13,"title":["Analysis of Testing\u2010Based Forward Model Selection"],"prefix":"10.3982","volume":"88","author":[{"given":"Damian","family":"Kozbur","sequence":"first","affiliation":[{"name":"Department of Economics, University of Z\u00fcrich"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"issue":"3","key":"ecta200183-bib-0001","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/2938229","volume":"59","author":"Andrews","year":"1991","journal-title":"Econometrica"},{"key":"ecta200183-bib-0002","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.jeconom.2008.08.010","volume":"146","author":"Bai","year":"2008","journal-title":"Journal of Econometrics"},{"issue":"2","key":"ecta200183-bib-0003","doi-asserted-by":"crossref","first-page":"521","DOI":"10.3150\/11-BEJ410","volume":"19","author":"Belloni","year":"2013","journal-title":"Bernoulli"},{"key":"ecta200183-bib-0004","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.3982\/ECTA9626","volume":"80","author":"Belloni","year":"2012","journal-title":"Econometrica"},{"issue":"2","key":"ecta200183-bib-0005","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1093\/restud\/rdt044","volume":"81","author":"Belloni","year":"2014","journal-title":"Review of Economic Studies"},{"issue":"4","key":"ecta200183-bib-0006","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1080\/07350015.2015.1102733","volume":"34","author":"Belloni","year":"2016","journal-title":"Journal of Business & Economic Statistics"},{"issue":"2","key":"ecta200183-bib-0007","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1214\/15-AOS1388","volume":"44","author":"Bertsimas","year":"2016","journal-title":"Annals of Statistics"},{"issue":"4","key":"ecta200183-bib-0008","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1214\/08-AOS620","volume":"37","author":"Bickel","year":"2009","journal-title":"Annals of Statistics"},{"issue":"2","key":"ecta200183-bib-0009","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1214\/009053606000000092","volume":"34","author":"B\u00fchlmann","year":"2006","journal-title":"Annals of Statistics"},{"key":"ecta200183-bib-0010","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-20192-9","volume-title":"Statistics for High-Dimensional Data: Methods, Theory and Applications","author":"B\u00fchlmann","year":"2011"},{"issue":"6","key":"ecta200183-bib-0011","doi-asserted-by":"crossref","first-page":"2313","DOI":"10.1214\/009053606000001523","volume":"35","author":"Cand\u00e8s","year":"2007","journal-title":"Annals of Statistics"},{"key":"ecta200183-bib-0012","unstructured":"Chetverikov, D., Z. Liao, and V. Chernozhukov (2016): \u201cOn Cross-Validated Lasso,\u201d ArXiv e-prints."},{"issue":"4","key":"ecta200183-bib-0013","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.3982\/ECTA14176","volume":"86","author":"Chudik","year":"2018","journal-title":"Econometrica"},{"key":"ecta200183-bib-0014","volume-title":"Proceedings of the 28th International Conference on Machine Learning (ICML-11)","author":"Das","year":"2011"},{"issue":"2","key":"ecta200183-bib-0015","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1214\/009053604000000067","volume":"32","author":"Efron","year":"2004","journal-title":"Annals of statistics"},{"key":"ecta200183-bib-0016","unstructured":"Efroymson, M. (1966): \u201cStepwise Regression\u2014A Backward and Forward Look,\u201d Florham Park, New Jersey."},{"issue":"1","key":"ecta200183-bib-0017","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/1468-0262.00399","volume":"71","author":"Elbers","year":"2003","journal-title":"Econometrica"},{"key":"ecta200183-bib-0018","doi-asserted-by":"crossref","DOI":"10.1596\/978-0-8213-7352-1","volume-title":"Conditional Cash Transfers: Reducing Present and Future Poverty","author":"Fiszbein","year":"2009"},{"key":"ecta200183-bib-0019","unstructured":"Fithian, W., J. Taylor, R. Tibshirani, and R. Tibshirani (2015): \u201cSelective Sequential Model Selection,\u201d ArXiv e-prints."},{"issue":"2","key":"ecta200183-bib-0020","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/00401706.1993.10485033","volume":"35","author":"Frank","year":"1993","journal-title":"Technometrics"},{"key":"ecta200183-bib-0021","first-page":"148","volume-title":"Proceedings of the Thirteenth International Conference on Machine Learning (ICML 1996)","author":"Freund","year":"1996"},{"key":"ecta200183-bib-0022","first-page":"1","volume":"8","author":"Grothendieck","year":"1953","journal-title":"Boletim Sociedade de Matem\u00e1tica de S\u00e3o Paulo"},{"issue":"2","key":"ecta200183-bib-0023","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1111\/rssb.12122","volume":"78","author":"G'Sell","year":"2016","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"3","key":"ecta200183-bib-0024","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s00440-015-0659-z","volume":"165","author":"Gu\u00e9don","year":"2016","journal-title":"Probability Theory and Related Fields"},{"issue":"4","key":"ecta200183-bib-0025","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1257\/jep.32.4.201","volume":"32","author":"Hanna","year":"2018","journal-title":"Journal of Economic Perspectives"},{"key":"ecta200183-bib-0026","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-84858-7","volume-title":"Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"Hastie","year":"2009"},{"key":"ecta200183-bib-0027","unstructured":"Hastie, T., R. Tibshirani, R. J. Tibshirani (2017): \u201cExtended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso,\u201d ArXiv e-prints."},{"issue":"4","key":"ecta200183-bib-0028","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1214\/09-AOS781","volume":"38","author":"Huang","year":"2010","journal-title":"Annals of Statistics"},{"key":"ecta200183-bib-0029","first-page":"2869","volume":"15","author":"Javanmard","year":"2014","journal-title":"Journal of Machine Learning Research"},{"issue":"4","key":"ecta200183-bib-0030","doi-asserted-by":"crossref","first-page":"2167","DOI":"10.1214\/aop\/1068646382","volume":"31","author":"Jing","year":"2003","journal-title":"Annals of Probability"},{"key":"ecta200183-bib-0031","doi-asserted-by":"crossref","unstructured":"Kozbur, D. (2017a): \u201cSharp Convergence Rates for Forward Regression in High-Dimensional Sparse Linear Models,\u201d ArXiv e-prints.","DOI":"10.2139\/ssrn.2973258"},{"issue":"5","key":"ecta200183-bib-0032","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1257\/aer.p20171039","volume":"107","author":"Kozbur","year":"2017","journal-title":"American Economic Review"},{"key":"ecta200183-bib-0033","doi-asserted-by":"crossref","unstructured":"Kozbur, D. (2020): \u201cSupplement to \u2018Analysis of Testing-Based Forward Model Selection\u2019,\u201d Econometrica Supplemental Material, 88, https:\/\/doi.org\/10.3982\/ECTA16273.","DOI":"10.3982\/ECTA16273"},{"issue":"2","key":"ecta200183-bib-0034","first-page":"338","volume":"24","author":"Leeb","year":"2008","journal-title":"Econometric Theory"},{"issue":"518","key":"ecta200183-bib-0035","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/01621459.2016.1180989","volume":"112","author":"Li","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"ecta200183-bib-0036","doi-asserted-by":"crossref","unstructured":"Luo, Y., and M. Spindler (2017): L2 Boosting for Economic Applications, ArXiv e-prints.","DOI":"10.1257\/aer.p20171040"},{"key":"ecta200183-bib-0037","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1214\/009053606000000281","volume":"34","author":"Meinshausen","year":"2006","journal-title":"Annals of Statistics"},{"issue":"3","key":"ecta200183-bib-0038","doi-asserted-by":"crossref","first-page":"703","DOI":"10.2307\/1913610","volume":"55","author":"Newey","year":"1987","journal-title":"Econometrica"},{"issue":"3","key":"ecta200183-bib-0039","first-page":"531","volume":"32","author":"Nichols","year":"2018","journal-title":"World Bank Economic Review"},{"key":"ecta200183-bib-0040","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1002\/cpa.20227","volume":"61","author":"Rudelson","year":"2008","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"ecta200183-bib-0041","doi-asserted-by":"crossref","first-page":"3434","DOI":"10.1109\/TIT.2013.2243201","volume":"59","author":"Rudelson","year":"2013","journal-title":"IEEE Transactions on Information Theory"},{"key":"ecta200183-bib-0042","unstructured":"Tao, T. (2014): \u201cWhen Is Correlation Transitive?\u201d https:\/\/terrytao.wordpress.com\/2014\/06\/05\/when-is-correlation-transitive\/."},{"key":"ecta200183-bib-0043","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani","year":"1996","journal-title":"Journal of the Royal Statistical Society: Series B"},{"key":"ecta200183-bib-0044","unstructured":"Tibshirani, R. J., J. Taylor, R. Lockhart, and R. Tibshirani (2014): \u201cExact Post-Selection Inference for Sequential Regression Procedures,\u201d ArXiv e-prints."},{"issue":"10","key":"ecta200183-bib-0045","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1109\/TIT.2004.834793","volume":"50","author":"Tropp","year":"2004","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"ecta200183-bib-0046","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1214\/14-AOS1221","volume":"42","author":"Geer","year":"2014","journal-title":"Annals of Statistics"},{"issue":"488","key":"ecta200183-bib-0047","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1198\/jasa.2008.tm08516","volume":"104","author":"Wang","year":"2009","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"ecta200183-bib-0048","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/1912934","volume":"48","author":"White","year":"1980","journal-title":"Econometrica"},{"issue":"4","key":"ecta200183-bib-0049","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1214\/07-AOS520","volume":"36","author":"Zhang","year":"2008","journal-title":"Annals of Statistics"},{"issue":"1","key":"ecta200183-bib-0050","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/rssb.12026","volume":"76","author":"Zhang","year":"2014","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"ecta200183-bib-0051","first-page":"555","volume":"10","author":"Zhang","year":"2009","journal-title":"Journal of Machine Learning"},{"issue":"7","key":"ecta200183-bib-0052","doi-asserted-by":"crossref","first-page":"4689","DOI":"10.1109\/TIT.2011.2146690","volume":"57","author":"Zhang","year":"2011","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T07:03:42Z","timestamp":1723619022000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA16273"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":52,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020]]}},"alternative-id":["10.3982\/ECTA16273"],"URL":"https:\/\/doi.org\/10.3982\/ecta16273","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2020]]}}}