{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T12:25:20Z","timestamp":1768998320686,"version":"3.49.0"},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T00:00:00Z","timestamp":1705881600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p>We consider inference for possibly misspecified GMM models based on possibly nonsmooth moment conditions. While it is well known that misspecified GMM estimators with smooth moments remain \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000385_inline1.png\"\/><jats:tex-math>\n$\\sqrt {n}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> consistent and asymptotically normal, globally misspecified nonsmooth GMM estimators are \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000385_inline2.png\"\/><jats:tex-math>\n$n^{1\/3}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> consistent when either the weighting matrix is fixed or when the weighting matrix is estimated at the \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000385_inline3.png\"\/><jats:tex-math>\n$n^{1\/3}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> rate or faster. Because the estimator\u2019s nonstandard asymptotic distribution cannot be consistently estimated using the standard bootstrap, we propose an alternative rate-adaptive bootstrap procedure that consistently estimates the asymptotic distribution regardless of whether the GMM estimator is smooth or nonsmooth, correctly or incorrectly specified. Monte Carlo simulations for the smooth and nonsmooth cases confirm that our rate-adaptive bootstrap confidence intervals exhibit empirical coverage close to the nominal level.<\/jats:p>","DOI":"10.1017\/s0266466623000385","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T06:49:02Z","timestamp":1706165342000},"page":"421-471","source":"Crossref","is-referenced-by-count":2,"title":["RATE-ADAPTIVE BOOTSTRAP FOR POSSIBLY MISSPECIFIED GMM"],"prefix":"10.1017","volume":"41","author":[{"given":"Han","family":"Hong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jessie","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,1,22]]},"reference":[{"key":"S0266466623000385_r33","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004394"},{"key":"S0266466623000385_r35","volume-title":"Asymptotic statistics","volume":"3","author":"van der Vaart","year":"2000"},{"key":"S0266466623000385_r13","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991978"},{"key":"S0266466623000385_r25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.05.008"},{"key":"S0266466623000385_r37","unstructured":"Wellner, J. 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