{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:35:12Z","timestamp":1785404112631,"version":"3.56.0"},"reference-count":41,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"abstract":"<jats:p>\n                    In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466626100334_inline1.png\"\/>\n                        <jats:tex-math>$l_0$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    on the direction of the parameter vector. We begin by establishing a general result that identifies this direction through the leading generalized eigenspace of specific measurable matrices. Using this result, we propose a novel approach to the selection of the best subsets by solving an empirical generalized eigenvalue problem to estimate the direction of the HD parameter. We then introduce a new estimator based on the RIFLE algorithm, providing a non-asymptotic bound for the estimation risk, minimax convergence, and a central limit theorem. Simulations demonstrate the superiority of our method over existing\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466626100334_inline2.png\"\/>\n                        <jats:tex-math>$l_0$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -constrained estimators.\n                  <\/jats:p>","DOI":"10.1017\/s0266466626100334","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T05:24:33Z","timestamp":1771910673000},"page":"1-39","source":"Crossref","is-referenced-by-count":0,"title":["DIRECTION IDENTIFICATION AND MINIMAX ESTIMATION IN HIGH-DIMENSIONAL SPARSE REGRESSION VIA A GENERALIZED EIGENVALUE APPROACH"],"prefix":"10.1017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2535-1002","authenticated-orcid":false,"given":"Mathieu","family":"Sauvenier","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02495e989","id-type":"ROR","asserted-by":"publisher"}],"name":"UCLouvain, Louvain-la-Neuve"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5648-5460","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Van Bellegem","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02495e989","id-type":"ROR","asserted-by":"publisher"}],"name":"UCLouvain, Louvain-la-Neuve"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,2,24]]},"reference":[{"key":"S0266466626100334_r5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596304010"},{"key":"S0266466626100334_r33","first-page":"1362","article-title":"Sparse generalized eigenvalue problem with application to canonical correlation analysis for integrative analysis of methylation and gene expression data","volume":"74","author":"Safo","year":"2018","journal-title":"Biometrics. 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