{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T02:41:00Z","timestamp":1792204860589,"version":"4.4.0"},"reference-count":50,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"vor","delay-in-days":187,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Sparsity in a regression context makes the model itself an object of interest, pointing to a confidence set of models as the appropriate presentation of the evidence. A difficulty in areas such as genomics, where the number of candidate variables is vast, arises from the need for preliminary reduction before the assessment of models. The present paper considers a resolution using inferential separations fundamental to the Fisherian approach to conditional inference, namely, the sufficiency\/co-sufficiency separation and the ancillary\/co-ancillary separation. Tests of model adequacy based on such separations do not involve specifying a direction of departure from any postulated model, avoiding calibration issues that would arise in directed tests from using the same data for reduction and for model assessment. In idealized cases with no nuisance parameters, the separations extract the relevant information without loss or redundancy. The extent to which estimation of nuisance parameters affects this idealization is illustrated in detail for the normal-theory linear regression model, extending immediately to a lognormal accelerated-life model for time-to-event outcomes. As part of the analysis, we introduce a modified version of the refitted cross-validation estimator of Fan et\u00a0al. (2012), whose distribution theory is tractable in the appropriate conditional sense. The paper concludes, among other things, that in settings where reduction on a reduced sample is unproblematic, sample splitting has high efficiency relative to our conditional analysis, echoing Cox (1975); otherwise, it gives miscalibrated confidence sets.<\/jats:p>","DOI":"10.1093\/biomet\/asag045","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T15:39:39Z","timestamp":1783438779000},"source":"Crossref","is-referenced-by-count":0,"title":["Post-reduction inference for confidence sets of models"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9387-4628","authenticated-orcid":false,"given":"H S","family":"Battey","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imperial College London , 180 Queen\u2019s Gate , London SW7 2AZ,","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1558-5860","authenticated-orcid":false,"given":"D G","family":"Rasines","sequence":"additional","affiliation":[{"name":"CUNEF Universidad , Calle Almansa 101 , Madrid 28040, daniel.garciarasines@cunef.edu","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6228-7049","authenticated-orcid":false,"given":"Y","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London , 180 Queen\u2019s Gate , London SW7 2AZ, . yanbo.tang@imperial.ac.uk","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,7,7]]},"reference":[{"key":"2026101621520634400_asag045-B1","doi-asserted-by":"crossref","first-page":"2514","DOI":"10.1214\/22-AOS2187","article-title":"Testing goodness of fit and conditional independence with approximate cosufficient subsampling","volume":"50","author":"Barber","year":"2022","journal-title":"Ann. 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