{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T14:56:28Z","timestamp":1787496988535,"version":"build-2736575974"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,15]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The classical likelihood ratio test based on the asymptotic chi-squared distribution of the log-likelihood is one of the fundamental tools of statistical inference. A recent universal likelihood ratio test approach based on sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute the split likelihood ratio statistic, or, more generally, an upper bound on the null maximum likelihood. The universal likelihood ratio test is valid in finite samples and without regularity conditions. This test empowers statisticians to construct tests in settings for which no valid hypothesis test previously existed. For the simple, but fundamental, case of testing the population mean of $d$-dimensional Gaussian data with an identity covariance matrix, the classical likelihood ratio test itself applies. Thus, this setting serves as a perfect test bed to compare the classical likelihood ratio test against the universal likelihood ratio test. This work presents the first in-depth exploration of the size, power and relationships between several universal likelihood ratio test variants. We show that a repeated subsampling approach is the best choice in terms of size and power. For large numbers of subsamples, the repeated subsampling set is approximately spherical. We observe reasonable performance even in a high-dimensional setting, where the expected squared radius of the best universal likelihood ratio test\u2019s confidence set is approximately 3\/2 times the squared radius of the classical likelihood ratio test\u2019s spherical confidence set. We illustrate the benefits of the universal likelihood ratio test through testing a nonconvex doughnut-shaped null hypothesis, where a universal inference procedure can have higher power than a standard approach.<\/jats:p>","DOI":"10.1093\/biomet\/asac064","type":"journal-article","created":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T16:39:53Z","timestamp":1668875993000},"page":"319-337","source":"Crossref","is-referenced-by-count":13,"title":["Gaussian universal likelihood ratio testing"],"prefix":"10.1093","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1620-0413","authenticated-orcid":false,"given":"Robin","family":"Dunn","sequence":"first","affiliation":[{"name":"Novartis Pharmaceuticals Corporation, Advanced Methodology and Data Science , 1 Health Plaza, East Hanover, New Jersey 07936, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0497-311X","authenticated-orcid":false,"given":"Aaditya","family":"Ramdas","sequence":"additional","affiliation":[{"name":"Department of Statistics & Data Science, Carnegie Mellon University , 132H Baker Hall, Pittsburgh, Pennsylvania 15213, U.S.A. aramdas@stat.cmu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sivaraman","family":"Balakrishnan","sequence":"additional","affiliation":[{"name":"Department of Statistics & Data Science, Carnegie Mellon University , 132H Baker Hall, Pittsburgh, Pennsylvania 15213, U.S.A. siva@stat.cmu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1874-5601","authenticated-orcid":false,"given":"Larry","family":"Wasserman","sequence":"additional","affiliation":[{"name":"Department of Statistics & Data Science, Carnegie Mellon University , 132H Baker Hall, Pittsburgh, Pennsylvania 15213, U.S.A. larry@stat.cmu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"2023051508570446600_B1","first-page":"268","article-title":"Properties of sufficiency and statistical tests","volume":"160","author":"Bartlett,","year":"1937","journal-title":"Proc. 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