{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T15:12:10Z","timestamp":1788189130569,"version":"build-2803163510"},"reference-count":21,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T00:00:00Z","timestamp":1598832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,2]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We study a class of parameters with the so-called mixed bias property. For parameters with this property, the bias of the semiparametric efficient one-step estimator is equal to the mean of the product of the estimation errors of two nuisance functions. In nonparametric models, parameters with the mixed bias property admit so-called rate doubly robust estimators, i.e., estimators that are consistent and asymptotically normal when one succeeds in estimating both nuisance functions at sufficiently fast rates, with the possibility of trading off slower rates of convergence for the estimator of one of the nuisance functions against faster rates for the estimator of the other nuisance function. We show that the class of parameters with the mixed bias property strictly includes two recently studied classes of parameters which, in turn, include many parameters of interest in causal inference. We characterize the form of parameters with the mixed bias property and of their influence functions. Furthermore, we derive two functional loss functions, each being minimized at one of the two nuisance functions. These loss functions can be used to derive loss-based penalized estimators of the nuisance functions.<\/jats:p>","DOI":"10.1093\/biomet\/asaa054","type":"journal-article","created":{"date-parts":[[2020,7,14]],"date-time":"2020-07-14T19:08:28Z","timestamp":1594753708000},"page":"231-238","source":"Crossref","is-referenced-by-count":36,"title":["Characterization of parameters with a mixed bias property"],"prefix":"10.1093","volume":"108","author":[{"given":"A","family":"Rotnitzky","sequence":"first","affiliation":[{"name":"Department of Economics, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, Buenos Aires 1428, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E","family":"Smucler","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, Buenos Aires 1428, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J M","family":"Robins","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, Harvard T. H. Chan School of Public Health, 655 Huntingdon Avenue, Boston, Massachusetts 02115, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,8,31]]},"reference":[{"key":"2021030708334520400_B1","author":"Chernozhukov,","year":"2018","journal-title":"Locally robust semiparametric estimation"},{"key":"2021030708334520400_B2","author":"Chernozhukov,","year":"2019","journal-title":"Learning L2 continuous regression functionals via regularized Riesz representers"},{"key":"2021030708334520400_B3","author":"Cui,","year":"2020","journal-title":"Selective machine learning of doubly robust functionals"},{"key":"2021030708334520400_B4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jeconom.2015.06.017","article-title":"Robust inference on average treatment effects with possibly more covariates than observations","volume":"189","author":"Farrell,","year":"2015","journal-title":"J. Economet."},{"key":"2021030708334520400_B5","author":"Hirshberg,","year":"2019","journal-title":"Augmented minimax linear estimation"},{"key":"2021030708334520400_B6","author":"Luedtke,","year":"2018","journal-title":"Sequential double robustness in right-censored longitudinal models"},{"key":"2021030708334520400_B7","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1093\/biomet\/asx027","article-title":"Multiple robustness in factorized likelihood models","volume":"104","author":"Molina,","year":"2017","journal-title":"Biometrika"},{"key":"2021030708334520400_B8","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1111\/j.1468-0262.2004.00518.x","article-title":"Twicing kernels and a small bias property of semiparametric estimators","volume":"72","author":"Newey,","year":"2004","journal-title":"Econometrica"},{"key":"2021030708334520400_B9","author":"Ning,","year":"2018","journal-title":"Robust estimation of causal effects via high-dimensional covariate balancing propensity score"},{"key":"2021030708334520400_B10","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1214\/193940307000000527","article-title":"Higher order influence functions and minimax estimation of nonlinear functionals","volume-title":"Probability and Statistics: Essays in Honor of David A. Freedman","author":"Robins,","year":"2008"},{"key":"2021030708334520400_B11","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1214\/16-AOS1515","article-title":"Minimax estimation of a functional on a structured high-dimensional model","volume":"45","author":"Robins,","year":"2017","journal-title":"Ann. Statist."},{"key":"2021030708334520400_B12","first-page":"920","article-title":"Comment on the Bickel and Kwon article \u2018Inference for semiparametric models: Some questions and an answer\u2019","volume":"11","author":"Robins,","year":"2001","journal-title":"Statist. Sinica"},{"key":"2021030708334520400_B13","author":"Rotnitzky,","year":"2017","journal-title":"On the multiply robust estimation of the mean of the g-functional"},{"key":"2021030708334520400_B14","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1080\/01621459.1999.10473862","article-title":"Adjusting for nonignorable drop-out using semiparametric nonresponse models","volume":"94","author":"Scharfstein,","year":"1999","journal-title":"J. Am. Statist. Assoc."},{"key":"2021030708334520400_B15","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1214\/aos\/1176350055","article-title":"On asymptotically efficient estimation in semiparametric models","volume":"14","author":"Schick,","year":"1986","journal-title":"Ann. Statist."},{"key":"2021030708334520400_B16","article-title":"A unifying approach for doubly-robust $\\ell_{1}$ regularized estimation of causal contrasts","author":"Smucler,","year":"2019"},{"key":"2021030708334520400_B17","author":"Tan,","year":"2018","journal-title":"Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data"},{"key":"2021030708334520400_B18","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1177\/009286150904300406","article-title":"A commentary on G. Molenberghs\u2019s review of missing data methods","volume":"43","author":"Tchetgen Tchetgen,","year":"2009","journal-title":"Drug Info. J."},{"key":"2021030708334520400_B19","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1214\/12-AOS990","article-title":"Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness, and sensitivity analysis","volume":"40","author":"Tchetgen Tchetgen,","year":"2012","journal-title":"Ann. Statist."},{"key":"2021030708334520400_B20","volume-title":"Asymptotic Statistics","author":"van der Vaart,","year":"2000"},{"key":"2021030708334520400_B21","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/978-1-4419-9782-1_27","article-title":"Cross-validated targeted minimum-loss-based estimation","volume-title":"Targeted Learning: Causal Inference for Observational and Experimental Data","author":"Zheng,","year":"2011"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaa054\/33702282\/asaa054.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/1\/231\/36441108\/asaa054.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/1\/231\/36441108\/asaa054.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,7]],"date-time":"2021-03-07T08:35:05Z","timestamp":1615106105000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/108\/1\/231\/5899828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,31]]},"references-count":21,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,8,31]]},"published-print":{"date-parts":[[2021,3,2]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa054","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,3,1]]},"published":{"date-parts":[[2020,8,31]]}}}