{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T09:29:58Z","timestamp":1789032598599,"version":"build-2803163510"},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:00:00Z","timestamp":1584576000000},"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":[[2020,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>This paper is concerned with empirical likelihood inference on the population mean when the dimension $p$ and the sample size $n$ satisfy $p\/n\\rightarrow c\\in [1,\\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p\/n&amp;gt;1\/2$ because the convex hull of the $n$ observations in $\\mathbb{R}^p$ becomes too small to cover the true mean value. Moreover, when $p&amp;gt; n$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data.<\/jats:p>","DOI":"10.1093\/biomet\/asaa005","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T12:09:57Z","timestamp":1579867797000},"page":"591-607","source":"Crossref","is-referenced-by-count":15,"title":["Empirical likelihood test for a large-dimensional mean vector"],"prefix":"10.1093","volume":"107","author":[{"given":"Xia","family":"Cui","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, 230 Wai Huan Xi Road, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Runze","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangren","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistics, School of Economics, Jinan University, 601 Huangpu W. Ave., Guangzhou 510632, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, National University of Singapore, 21 Lower Kent Ridge Road, 117546 Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,3,19]]},"reference":[{"key":"2020081714264587700_B1","first-page":"311","article-title":"Effect of high dimension: By an example of a two sample problem","volume":"6","author":"Bai,","year":"1996","journal-title":"Statist. Sinica"},{"key":"2020081714264587700_B2","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1214\/aop\/1176989118","article-title":"Limit of the smallest eigenvalue of a large dimensional sample covariance matrix","volume":"21","author":"Bai,","year":"1993","journal-title":"Ann. 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Assoc."}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/3\/591\/33658410\/asaa005.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/3\/591\/33658410\/asaa005.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,17]],"date-time":"2020-08-17T18:45:37Z","timestamp":1597689937000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/107\/3\/591\/5810170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,19]]},"references-count":16,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3,19]]},"published-print":{"date-parts":[[2020,9,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa005","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2020,3,19]]}}}