{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T22:02:10Z","timestamp":1781820130951,"version":"3.54.5"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,9,14]],"date-time":"2020-09-14T00:00:00Z","timestamp":1600041600000},"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":[[2021,8,12]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. The conclusion that bootstrap samples should be of smaller size than the original sample has significant implications for computational efficiency and scalability of bootstrap methodologies with dependent data. Our main theorem determines the optimal number of blocks and block length to achieve the best possible convergence rate for the block bootstrap distribution estimator for sample quantiles. We propose an intuitive method for empirical selection of the optimal number and length of blocks, and demonstrate its value in a nontrivial example.<\/jats:p>","DOI":"10.1093\/biomet\/asaa075","type":"journal-article","created":{"date-parts":[[2020,9,2]],"date-time":"2020-09-02T19:14:49Z","timestamp":1599074089000},"page":"675-692","source":"Crossref","is-referenced-by-count":5,"title":["Block bootstrap optimality and empirical block selection for sample quantiles with dependent data"],"prefix":"10.1093","volume":"108","author":[{"given":"T A","family":"Kuffner","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S M S","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G A","family":"Young","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,14]]},"reference":[{"key":"2021081218511463900_B1","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/BF02517808","article-title":"On the asymptotic accuracy of the bootstrap under arbitrary resampling size","volume":"55","author":"Arcones,","year":"2003","journal-title":"Ann. 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