{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:55:12Z","timestamp":1760234112772,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Hellinger distance has been widely used to derive objective functions that are alternatives to maximum likelihood methods. While the asymptotic distributions of these estimators have been well investigated, the probabilities of rare events induced by them are largely unknown. In this article, we analyze these rare event probabilities using large deviation theory under a potential model misspecification, in both one and higher dimensions. We show that these probabilities decay exponentially, characterizing their decay via a \u201crate function\u201d which is expressed as a convex conjugate of a limiting cumulant generating function. In the analysis of the lower bound, in particular, certain geometric considerations arise that facilitate an explicit representation, also in the case when the limiting generating function is nondifferentiable. Our analysis involves the modulus of continuity properties of the affinity, which may be of independent interest.<\/jats:p>","DOI":"10.3390\/e23040386","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T15:42:19Z","timestamp":1616600539000},"page":"386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Rare Event Analysis for Minimum Hellinger Distance Estimators via Large Deviation Theory"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8645-6372","authenticated-orcid":false,"given":"Anand N.","family":"Vidyashankar","sequence":"first","affiliation":[{"name":"Department of Statistics, George Mason University, Fairfax, VA 22030, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6372-8152","authenticated-orcid":false,"given":"Jeffrey F.","family":"Collamore","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1214\/aos\/1176343842","article-title":"Minimum Hellinger distance estimates for parametric models","volume":"5","author":"Beran","year":"1977","journal-title":"Ann. 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