{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T10:06:23Z","timestamp":1780394783458,"version":"3.54.1"},"reference-count":31,"publisher":"The Econometric Society","issue":"3","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"}]},{"DOI":"10.13039\/501100001732","name":"Danmarks Grundforskningsfond","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001732","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>Certain extremum estimators have asymptotic distributions that are non\u2010Gaussian, yet characterizable as the distribution of the arg\u2009max of a Gaussian process. This paper presents high\u2010level sufficient conditions under which such asymptotic distributions admit a continuous distribution function. The plausibility of the sufficient conditions is demonstrated by verifying them in three examples, namely, maximum score estimation, empirical risk minimization, and threshold regression estimation. In turn, the continuity result buttresses several recently proposed inference procedures whose validity seems to require a result of the kind established herein. A notable feature of the high\u2010level assumptions is that one of them is designed to enable us to employ the Cameron\u2013Martin theorem. In a leading special case, the assumption in question is demonstrably weak and appears to be close to minimal.<\/jats:p>","DOI":"10.3982\/ecta23862","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T09:09:52Z","timestamp":1780391392000},"page":"941-955","source":"Crossref","is-referenced-by-count":0,"title":["Continuity of the Distribution Function of the argmax of a Gaussian Process"],"prefix":"10.3982","volume":"94","author":[{"given":"Matias D.","family":"Cattaneo","sequence":"first","affiliation":[{"name":"Department of Operations Research and Financial Engineering, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory F.","family":"Cox","sequence":"additional","affiliation":[{"name":"Department of Economics, National University of Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Jansson","sequence":"additional","affiliation":[{"name":"Department of Economics, UC 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