{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T21:46:34Z","timestamp":1785793594713,"version":"3.56.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T00:00:00Z","timestamp":1710460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Research Grants Council of Hong Kong","award":["GRF-14500822"],"award-info":[{"award-number":["GRF-14500822"]}]},{"name":"Research Grant Council of the Hong Kong","award":["GRF-14303622"],"award-info":[{"award-number":["GRF-14303622"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the \u2018sparsest rule\u2019, which is equivalent to the plurality rule but becomes operational in computation algorithms, we investigate and prove the advantages of non-convex penalized approaches over other IV estimators based on two-step selections, in terms of selection consistency and accommodation for individually weak IVs. Furthermore, we propose a surrogate sparsest penalty that aligns with the identification condition and provides oracle sparse structure simultaneously. Desirable theoretical properties are derived for the proposed estimator with weaker IV strength conditions compared to the previous literature. Finite sample properties are demonstrated using simulations and the selection and estimation method is applied to an empirical study concerning the effect of body mass index on diastolic blood pressure.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae025","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T16:21:00Z","timestamp":1710519660000},"page":"1068-1088","source":"Crossref","is-referenced-by-count":11,"title":["On the instrumental variable estimation with many weak and invalid instruments"],"prefix":"10.1093","volume":"86","author":[{"given":"Yiqi","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong , Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4232-2783","authenticated-orcid":false,"given":"Frank","family":"Windmeijer","sequence":"additional","affiliation":[{"name":"Department of Statistics and Nuffield College, University 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