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Moreover, and perhaps related to their performance, nonoptimal windows are selected with undersmoothing needed to ensure the appropriate bias order. In this paper, we propose a recursive differencing estimator for conditional expectations. When this method is combined with a bias control targeting the derivative of the semiparametric expectation, we are able to obtain asymptotic normality under optimal windows. As suggested by the structure of the recursion, in a wide variety of triple index designs, the proposed bias control performs much better at moderate sample sizes than regular or higher-order kernels and local polynomials.<\/jats:p>","DOI":"10.1017\/s0266466622000329","type":"journal-article","created":{"date-parts":[[2022,8,18]],"date-time":"2022-08-18T08:38:48Z","timestamp":1660811928000},"page":"37-59","source":"Crossref","is-referenced-by-count":0,"title":["RECURSIVE DIFFERENCING FOR ESTIMATING SEMIPARAMETRIC MODELS"],"prefix":"10.1017","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5680-3134","authenticated-orcid":false,"given":"Chan","family":"Shen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0962-8019","authenticated-orcid":false,"given":"Roger","family":"Klein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,8,18]]},"reference":[{"key":"S0266466622000329_r6","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2014.956615"},{"key":"S0266466622000329_r15","doi-asserted-by":"publisher","DOI":"10.2307\/2951556"},{"key":"S0266466622000329_r2","first-page":"312","article-title":"Endogeneity in nonparametric and semiparametric regression models","volume":"36","author":"Blundell","year":"2003","journal-title":"Econometric Society Monographs"},{"key":"S0266466622000329_r4","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1080\/10618600.1995.10474678","article-title":"Adaptive order polynomial fitting: Bandwidth Robustification and bias reduction","volume":"4","author":"Fan","year":"1995","journal-title":"Journal of Computational and Graphical Statistics"},{"volume-title":"Nonparametric and Semiparametric Methods in Econometrics and Statistics","year":"1991","author":"Ichimura","key":"S0266466622000329_r11"},{"key":"S0266466622000329_r17","first-page":"444","volume-title":"The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics","author":"Li","year":"2014"},{"key":"S0266466622000329_r21","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346523"},{"key":"S0266466622000329_r22","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00518.x"},{"volume-title":"Local Polynomial Modeling and Its Applications","year":"1996","author":"Fan","key":"S0266466622000329_r5"},{"key":"S0266466622000329_r26","doi-asserted-by":"publisher","DOI":"10.2307\/1912705"},{"key":"S0266466622000329_r3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-937X.2004.00299.x"},{"key":"S0266466622000329_r20","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00097"},{"key":"S0266466622000329_r18","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1996.0060"},{"key":"S0266466622000329_r23","first-page":"2111","volume-title":"Handbook of Econometrics","volume":"4","author":"Newey","year":"1994"},{"key":"S0266466622000329_r28","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00232"},{"key":"S0266466622000329_r10","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(93)90114-K"},{"key":"S0266466622000329_r19","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(96)00095-6"},{"key":"S0266466622000329_r14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.10.006"},{"key":"S0266466622000329_r9","doi-asserted-by":"publisher","DOI":"10.2307\/2171926"},{"key":"S0266466622000329_r25","doi-asserted-by":"publisher","DOI":"10.2307\/1913713"},{"key":"S0266466622000329_r27","first-page":"1346","article-title":"Multivariate locally weighted least-squares regression","volume":"52","author":"Ruppert","year":"1994","journal-title":"Annals of Statistics"},{"key":"S0266466622000329_r13","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990764"},{"key":"S0266466622000329_r8","first-page":"520","volume-title":"Identification and Inference in Econometric Models. 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