{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T16:38:58Z","timestamp":1768322338774,"version":"3.49.0"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T00:00:00Z","timestamp":1604448000000},"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":[[2021,11,15]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Hall &amp; Robinson (2009) proposed and analysed the use of bagged cross-validation to choose the bandwidth of a kernel density estimator. They established that bagging greatly reduces the noise inherent in ordinary cross-validation, and hence leads to a more efficient bandwidth selector. The asymptotic theory of Hall &amp; Robinson (2009) assumes that $N$, the number of bagged subsamples, is $\\infty$. We expand upon their theoretical results by allowing $N$ to be finite, as it is in practice. Our results indicate an important difference in the rate of convergence of the bagged cross-validation bandwidth for the cases $N=\\infty$ and $N&amp;lt;\\infty$. Simulations quantify the improvement in statistical efficiency and computational speed that can result from using bagged cross-validation as opposed to a binned implementation of ordinary cross-validation. The performance of the bagged bandwidth is also illustrated on a real, very large, dataset. Finally, a byproduct of our study is the correction of errors appearing in the Hall &amp; Robinson (2009) expression for the asymptotic mean squared error of the bagging selector.<\/jats:p>","DOI":"10.1093\/biomet\/asaa092","type":"journal-article","created":{"date-parts":[[2020,10,19]],"date-time":"2020-10-19T19:14:16Z","timestamp":1603134856000},"page":"981-988","source":"Crossref","is-referenced-by-count":6,"title":["Bagging cross-validated bandwidths with application to big data"],"prefix":"10.1093","volume":"108","author":[{"given":"D","family":"Barreiro-Ures","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultade de Inform\u00e1tica, CITIC, Universidade da Coru\u00f1a, Campus de Elvi\u00f1a, 15071 A Coru\u00f1a, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R","family":"Cao","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultade de Inform\u00e1tica, CITIC, Universidade da Coru\u00f1a, Campus de Elvi\u00f1a, 15071 A Coru\u00f1a, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M","family":"Francisco-Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultade de Inform\u00e1tica, CITIC, Universidade da Coru\u00f1a, Campus de Elvi\u00f1a, 15071 A Coru\u00f1a, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J D","family":"Hart","sequence":"additional","affiliation":[{"name":"Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"2021111803493649100_B1","article-title":"baggedcv: Bagged cross-validation for kernel density bandwidth selection","author":"Barreiro-Ures,","year":"2019","journal-title":"R package version 1.0"},{"key":"2021111803493649100_B2","article-title":"Partitioned cross-validation for divide-and conquer density estimation","author":"Bhattacharya,","year":"2016"},{"key":"2021111803493649100_B3","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1006\/jmva.1993.1030","article-title":"Bootstrapping the mean integrated squared error","volume":"45","author":"Cao,","year":"1993","journal-title":"J. Mult. Anal."},{"key":"2021111803493649100_B4","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0167-9473(92)90002-W","article-title":"A note on modified cross-validation in density estimation","volume":"13","author":"Feluch,","year":"1992","journal-title":"Comp. Statist. Data Anal."},{"key":"2021111803493649100_B5","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.jspi.2006.06.002","article-title":"On bagging and nonlinear estimation","volume":"137","author":"Friedman,","year":"2007","journal-title":"J. Statist. Plan. Infer."},{"key":"2021111803493649100_B6","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/BF00363516","article-title":"Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation","volume":"74","author":"Hall,","year":"1987","journal-title":"Prob. Theory Rel. 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