{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T12:12:28Z","timestamp":1778069548030,"version":"3.51.4"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"vor","delay-in-days":62,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We characterize the behaviour of the maximum Diaconis\u2013Ylvisaker prior penalized likelihood estimator in high-dimensional logistic regression, where the number of covariates is a fraction $ \\kappa\\in(0,1) $ of the number of observations $ n $, as $ n\\to\\infty $. We construct a rescaled estimator with zero asymptotic aggregate bias, and define adjusted $ Z $-statistics and rescaled penalized likelihood ratio statistics that exhibit the typical null asymptotic distributions, when the covariates are independent multivariate normal with an arbitrary covariance matrix and the linear predictor has asymptotic variance $ \\gamma^{2} $. While the maximum likelihood estimate asymptotically exists only for a narrow range of $ (\\kappa,\\gamma) $ values, the maximum Diaconis\u2013Ylvisaker prior penalized likelihood estimate always exists and can be computed directly using standard maximum likelihood routines. Thus, our asymptotic results extend to $ (\\kappa,\\gamma) $ values for which the maximum likelihood framework breaks down, with no additional implementation or computational cost. We study the estimator\u2019s shrinkage properties, compare the proposed estimation and inference procedures with alternatives that also accommodate proportional asymptotics, and formulate a conjecture, supported by strong empirical evidence, that extends our results to models including an intercept parameter. Finally, we propose estimation methods for all unknown constants involved in our procedures and demonstrate the theoretical advances through extensive simulation studies and the analysis of digit recognition data.<\/jats:p>","DOI":"10.1093\/biomet\/asag014","type":"journal-article","created":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T12:27:38Z","timestamp":1771331258000},"source":"Crossref","is-referenced-by-count":0,"title":["Diaconis\u2013Ylvisaker prior penalized likelihood for $ p\/n\\to\\kappa\\in(0,1) $ logistic regression"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7348-5810","authenticated-orcid":false,"given":"P","family":"Sterzinger","sequence":"first","affiliation":[{"name":"Department of Statistics, London School of Economics and Political Science, Houghton Street , London WC2A 2AE,","place":["U.K"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1556-0302","authenticated-orcid":false,"given":"I","family":"Kosmidis","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Warwick , Gibbet Hill Road , Coventry, CV4 7AL, . i.kosmidis@warwick.ac.uk","place":["U.K"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,3,3]]},"reference":[{"key":"2026050607162684800_asag014-B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/biomet\/71.1.1","article-title":"On the existence of maximum likelihood estimates in logistic regression models","volume":"71","author":"Albert","year":"1984","journal-title":"Biometrika"},{"key":"2026050607162684800_asag014-B3","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1214\/14-AAP1010","article-title":"Universality in polytope phase transitions and message passing algorithms","volume":"25","author":"Bayati","year":"2015","journal-title":"Ann. 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