{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:38:54Z","timestamp":1765355934681,"version":"3.37.3"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2015,5,21]],"date-time":"2015-05-21T00:00:00Z","timestamp":1432166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-11-04545"],"award-info":[{"award-number":["DMS-11-04545"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007165","name":"University of Missouri","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007165","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,3,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide a more accurate approximation to the finite sample distribution than the conventional \u03c72-approximation. Our theoretical and numerical findings suggest that both the finite sample and the large sample upper bounds for coverage probabilities are strictly less than 1 and the blockwise empirical likelihood confidence region can exhibit serious undercoverage when the dimension of moment conditions is moderate or large, the time series dependence is positively strong or the block size is large relative to the sample size. A similar finite sample coverage problem occurs for non-standard expansive empirical likelihood. To alleviate the coverage bound problem, we propose to penalize both empirical likelihood methods by relaxing the convex hull constraint. Numerical simulations and data illustrations demonstrate the effectiveness of our proposed remedies in terms of delivering confidence sets with more accurate coverage. Some technical details and additional simulation results are included in on-line supplemental material.<\/jats:p>","DOI":"10.1111\/rssb.12119","type":"journal-article","created":{"date-parts":[[2015,5,21]],"date-time":"2015-05-21T17:13:52Z","timestamp":1432228432000},"page":"395-421","source":"Crossref","is-referenced-by-count":3,"title":["On the Coverage Bound Problem of Empirical Likelihood Methods for Time Series"],"prefix":"10.1093","volume":"78","author":[{"given":"Xianyang","family":"Zhang","sequence":"first","affiliation":[{"name":"University of Missouri\u2014Columbia \u00a0 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Shao","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign , Champaign , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2015,5,21]]},"reference":[{"key":"2023021709303549400_rssb12119-cit-0001","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.spl.2006.05.016","article-title":"A penalized version of the empirical likelihood ratio for the population mean","volume":"77","author":"Bartolucci","year":"2007","journal-title":"Statist. Probab. Lett."},{"key":"2023021709303549400_rssb12119-cit-0002","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316962","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1999"},{"key":"2023021709303549400_rssb12119-cit-0003","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.jeconom.2014.10.011","article-title":"High dimensional empirical likelihood for generalized estimating equations with dependent data","volume":"185","author":"Chang","year":"2015","journal-title":"J. Econmetr."},{"key":"2023021709303549400_rssb12119-cit-0004","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1093\/biomet\/93.1.215","article-title":"On Bartlett correction of empirical likelihood in the presence of nuisance parameters","volume":"93","author":"Chen","year":"2006","journal-title":"Biometrika"},{"key":"2023021709303549400_rssb12119-cit-0005","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1080\/10485252.2012.738906","article-title":"Finite-sample properties of the adjusted empirical likelihood","volume":"25","author":"Chen","year":"2012","journal-title":"J. Nonparam. Statist."},{"key":"2023021709303549400_rssb12119-cit-0006","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1198\/106186008X321068","article-title":"Adjusted empirical likelihood and its properties","volume":"17","author":"Chen","year":"2008","journal-title":"J. Computnl Graph. Statist."},{"key":"2023021709303549400_rssb12119-cit-0007","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1214\/aos\/1176348137","article-title":"Empirical likelihood is Bartlett-correctable","volume":"19","author":"Diciccio","year":"1991","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0008","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1214\/09-EJS518","article-title":"Calibration of the empirical likelihood method for a vector mean","volume":"3","author":"Emerson","year":"2009","journal-title":"Electron. J. Statist."},{"key":"2023021709303549400_rssb12119-cit-0009","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1017\/S0266466610000496","article-title":"Block bootstrap HAC robust tests: the sophistication of the naive bootstrap","volume":"27","author":"Gon\u00e7alves","year":"2011","journal-title":"Econmetr. Theor."},{"volume-title":"Trends: a Compendium of Data on Global Change","year":"2011","author":"Jones","key":"2023021709303549400_rssb12119-cit-0010"},{"key":"2023021709303549400_rssb12119-cit-0011","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.2140\/pjm.1959.9.1141","article-title":"Coincidence probabilities","volume":"9","author":"Karlin","year":"1959","journal-title":"Pacif. J. Math."},{"key":"2023021709303549400_rssb12119-cit-0012","first-page":"1130","article-title":"A new asymptotic theory for heteroskedasticity-autocorrelation robust tests","volume":"21","author":"Kiefer","year":"2005","journal-title":"Econmetr. Theor."},{"key":"2023021709303549400_rssb12119-cit-0013","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1080\/01621459.2013.847374","article-title":"A progressive block empirical likelihood method for time series","volume":"108","author":"Kim","year":"2013","journal-title":"J. Am. Statist. Ass."},{"key":"2023021709303549400_rssb12119-cit-0014","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1214\/aos\/1069362388","article-title":"Empirical likelihood methods with weakly dependent processes","volume":"25","author":"Kitamura","year":"1997","journal-title":"Ann. Statist."},{"volume-title":"Empirical likelihood methods in econometrics: theory and practice","year":"2006","author":"Kitamura","key":"2023021709303549400_rssb12119-cit-0015"},{"key":"2023021709303549400_rssb12119-cit-0016","first-page":"413","article-title":"On the asymptotic optimality of empirical likelihood for testing moment restrictions","volume":"80","author":"Kitamura","year":"2013","journal-title":"Econometrica"},{"key":"2023021709303549400_rssb12119-cit-0017","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1214\/12-AOS1040","article-title":"A penalized empirical likelihood method in high dimensions","volume":"40","author":"Lahiri","year":"2012","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0018","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1214\/09-AOS750","article-title":"Adjusted empirical likelihood with high-order precision","volume":"38","author":"Liu","year":"2010","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0019","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1214\/009053607000000064","article-title":"Computer-intensive rate estimation, diverging statistics, and scanning","volume":"35","author":"McElroy","year":"2007","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0020","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1093\/biomet\/asn071","article-title":"Tapered empirical likelihood for time series data in time and frequency domains","volume":"96","author":"Nordman","year":"2009","journal-title":"Biometrika"},{"key":"2023021709303549400_rssb12119-cit-0021","first-page":"3050","article-title":"A non-standard empirical likelihood for time series","volume":"4","author":"Nordman","year":"2013","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0022","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1198\/016214507000001391","article-title":"Point and interval estimation of variogram models using spatial empirical likelihood","volume":"103","author":"Nordman","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023021709303549400_rssb12119-cit-0023","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jspi.2013.10.001","article-title":"A review of empirical likelihood methods for time series","volume":"155","author":"Nordman","year":"2014","journal-title":"J. Statist. Planng Inf."},{"key":"2023021709303549400_rssb12119-cit-0024","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1016\/j.jmva.2007.05.005","article-title":"Penalized empirical likelihood estimation of semiparametric models","volume":"98","author":"Otsu","year":"2007","journal-title":"J. Multiv. Anal."},{"key":"2023021709303549400_rssb12119-cit-00105","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1093\/biomet\/75.2.237","article-title":"Empirical likelihood ratio confidence intervals for a single functional","volume":"75","author":"Owen","year":"1988","journal-title":"Biometrika"},{"key":"2023021709303549400_rssb12119-cit-0025","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1214\/aos\/1176347494","article-title":"Empirical likelihood confidence regions","volume":"18","author":"Owen","year":"1990","journal-title":"Ann. Statist."},{"volume-title":"Empirical Likelihood","year":"2001","author":"Owen","key":"2023021709303549400_rssb12119-cit-0026"},{"key":"2023021709303549400_rssb12119-cit-0027","doi-asserted-by":"crossref","first-page":"277","DOI":"10.2307\/1913237","article-title":"Time series regression with unit roots","volume":"55","author":"Phillips","year":"1987","journal-title":"Econometrica"},{"key":"2023021709303549400_rssb12119-cit-0028","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1175\/JCLI3637.1","article-title":"Improved analyses of changes and uncertainties in marine temperature measured in situ since the mid-nineteenth century: the HadSST2 dataset","volume":"19","author":"Rayner","year":"2006","journal-title":"J. Clim."},{"key":"2023021709303549400_rssb12119-cit-0029","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"Rockafellar","year":"1970"},{"key":"2023021709303549400_rssb12119-cit-0030","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1111\/j.1467-9868.2009.00737.x","article-title":"A self-normalized approach to confidence interval construction in time series","volume":"72","author":"Shao","year":"2010","journal-title":"J. R. Statist. Soc. B"},{"key":"2023021709303549400_rssb12119-cit-0031","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1214\/aoms\/1177693323","article-title":"First passage time for a particular Gaussian process","volume":"42","author":"Shepp","year":"1971","journal-title":"Ann. Math. Statist."},{"key":"2023021709303549400_rssb12119-cit-0032","doi-asserted-by":"crossref","DOI":"10.2139\/ssrn.2277234","volume-title":"Fixed-smoothing asymptotics in a two-step GMM framework","author":"Sun","year":"2013"},{"key":"2023021709303549400_rssb12119-cit-0033","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1093\/biomet\/asq057","article-title":"Penalized high-dimensional empirical likelihood","volume":"97","author":"Tang","year":"2010","journal-title":"Biometrika"},{"key":"2023021709303549400_rssb12119-cit-0034","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1214\/009053604000000337","article-title":"Bounds on coverage probabilities of the empirical likelihood ratio confidence regions","volume":"32","author":"Tsao","year":"2004","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0035","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.1214\/13-AOS1143","article-title":"Empirical likelihood on the full parameter space","volume":"41","author":"Tsao","year":"2013","journal-title":"Ann. Statist."},{"key":"2023021709303549400_rssb12119-cit-0036","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1093\/biomet\/asu014","article-title":"Extended empirical likelihood for estimating equations","volume":"101","author":"Tsao","year":"2014","journal-title":"Biometrika"},{"key":"2023021709303549400_rssb12119-cit-0038","first-page":"1179","article-title":"Fixed-b asymptotics for blockwise empirical likelihood","volume":"24","author":"Zhang","year":"2014","journal-title":"Statist. Sin."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12119","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/78\/2\/395\/49234976\/jrsssb_78_2_395.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/78\/2\/395\/49234976\/jrsssb_78_2_395.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T09:48:44Z","timestamp":1676627324000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/78\/2\/395\/7040651"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,21]]},"references-count":38,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,5,21]]},"published-print":{"date-parts":[[2016,3,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12119","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"type":"print","value":"1369-7412"},{"type":"electronic","value":"1467-9868"}],"subject":[],"published-other":{"date-parts":[[2016,3]]},"published":{"date-parts":[[2015,5,21]]}}}