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We show that the rate of the correction for nuisance parameters is larger than the correction for non-normality, when the parameter dimension p is O(n\u03b1) for \u03b1&amp;lt;12. We specialize the results to linear exponential families and location\u2013scale families and illustrate these with simulations.<\/jats:p>","DOI":"10.1111\/rssb.12389","type":"journal-article","created":{"date-parts":[[2020,8,2]],"date-time":"2020-08-02T10:39:45Z","timestamp":1596364785000},"page":"1349-1369","source":"Crossref","is-referenced-by-count":5,"title":["Modified Likelihood root in High Dimensions"],"prefix":"10.1093","volume":"82","author":[{"given":"Yanbo","family":"Tang","sequence":"first","affiliation":[{"name":"University of Toronto and Vector Institute , Toronto , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nancy","family":"Reid","sequence":"additional","affiliation":[{"name":"University of Toronto \u00a0 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,8,2]]},"reference":[{"key":"2023022408373498200_","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1093\/biomet\/70.2.343","article-title":"On a formula for the distribution of the maximum likelihood estimator","volume":"70","author":"Barndorff-Nielsen","year":"1983","journal-title":"Biometrika"},{"key":"2023022408373498200_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3210-5","volume-title":"Inference and Asymptotics","author":"Barndorff-Nielsen","year":"1994"},{"key":"2023022408373498200_","first-page":"268","article-title":"Properties of sufficiency and statistical tests","volume":"160","author":"Bartlett","year":"1937","journal-title":"Proc. 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