{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T16:11:03Z","timestamp":1760199063317,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T00:00:00Z","timestamp":1544659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["Grant 18-01137S"],"award-info":[{"award-number":["Grant 18-01137S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider the likelihood ratio test of a simple null hypothesis (with density     f 0    ) against a simple alternative hypothesis (with density     g 0    ) in the situation that observations     X i     are mismeasured due to the presence of measurement errors. Thus instead of     X i     for     i = 1 , \u2026 , n ,     we observe      Z i  =  X i  +  \u03b4   V i      with unobservable parameter    \u03b4    and unobservable random variable     V i    . When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.<\/jats:p>","DOI":"10.3390\/e20120966","type":"journal-article","created":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T03:58:17Z","timestamp":1544759897000},"page":"966","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Likelihood Ratio Testing under Measurement Errors"],"prefix":"10.3390","volume":"20","author":[{"given":"Michel","family":"Broniatowski","sequence":"first","affiliation":[{"name":"Facult\u00e9 de Math\u00e9matiques, Laboratoire de Probabilit\u00e9, Statistique et Mod\u00e9lisation, Universit\u00e9 Pierre et Marie Curie (Sorbonne Universit\u00e9), 4 place Jussieu, 75252 Paris CEDEX 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jana","family":"Jure\u010dkov\u00e1","sequence":"additional","affiliation":[{"name":"Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 4, 182 08 Prague 8, Czech Republic"},{"name":"Faculty of Mathematics and Physics, Charles University, Sokolovsk\u00e1 83, 186 75 Prague 8, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8491-0364","authenticated-orcid":false,"given":"Jan","family":"Kalina","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, The Czech Academy of Sciences, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07 Prague 8, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"629","DOI":"10.3102\/1076998613508584","article-title":"Measuring test measurement error: A general approach","volume":"38","author":"Boyd","year":"2013","journal-title":"J. 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