{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T20:42:36Z","timestamp":1790628156303,"version":"4.1.0"},"reference-count":42,"publisher":"The Econometric Society","issue":"6","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005969","name":"Universit\u00e0 di Bologna","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005969","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004836","name":"Det Frie Forskningsr\u00e5d","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004836","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the unconditional limit distribution of a statistic can be obtained by averaging a (random) limiting bootstrap distribution. Further, we provide results ensuring the asymptotic validity of the bootstrap as a tool for conditional inference, the leading case being that where a bootstrap distribution estimates consistently a conditional (and thus, random) limit distribution of a statistic. We apply our framework to several inference problems in econometrics, including linear models with possibly nonstationary regressors, CUSUM statistics, conditional Kolmogorov\u2013Smirnov specification tests and tests for constancy of parameters in dynamic econometric models.<\/jats:p>","DOI":"10.3982\/ecta16557","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T13:43:08Z","timestamp":1605620588000},"page":"2547-2574","source":"Crossref","is-referenced-by-count":36,"title":["Inference Under Random Limit Bootstrap Measures"],"prefix":"10.3982","volume":"88","author":[{"given":"Giuseppe","family":"Cavaliere","sequence":"first","affiliation":[{"name":"Department of Economics, University of Bologna"},{"name":"Department of Economics, University of Exeter"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iliyan","family":"Georgiev","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Bologna"},{"name":"Institut d'An\u00e0lisi Econ\u00f2mica\u2014CSIC"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"key":"ecta200218-bib-0001","doi-asserted-by":"crossref","first-page":"821","DOI":"10.2307\/2951764","volume":"61","author":"Andrews","year":"1993","journal-title":"Econometrica"},{"key":"ecta200218-bib-0002","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.2307\/2171880","volume":"65","author":"Andrews","year":"1997","journal-title":"Econometrica"},{"key":"ecta200218-bib-0003","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1111\/1468-0262.00114","volume":"68","author":"Andrews","year":"2000","journal-title":"Econometrica"},{"key":"ecta200218-bib-0004","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1214\/aos\/1176350371","volume":"15","author":"Athreya","year":"1987","journal-title":"The Annals of Statistics"},{"key":"ecta200218-bib-0005","doi-asserted-by":"crossref","first-page":"125","DOI":"10.3150\/07-BEJ6014","volume":"14","author":"Aue","year":"2008","journal-title":"Bernoulli"},{"key":"ecta200218-bib-0006","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3210-5","volume-title":"Inference and Asymptotics","author":"Barndorff-Nielsen","year":"1994"},{"key":"ecta200218-bib-0007","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1214\/aos\/1176348142","volume":"19","author":"Basawa","year":"1991","journal-title":"The Annals of Statistics"},{"key":"ecta200218-bib-0008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1003114420352","volume":"49","author":"Beran","year":"1997","journal-title":"The Annals of the Institute of Statistical Mathematics"},{"key":"ecta200218-bib-0009","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"ecta200218-bib-0010","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.3982\/ECTA17950","volume":"88","author":"Cattaneo","year":"2020","journal-title":"Econometrica"},{"key":"ecta200218-bib-0011","doi-asserted-by":"crossref","unstructured":"Cavaliere, G., and I. Georgiev (2020): \u201cSupplement to \u2018Inference Under Random Limit Bootstrap Measures\u2019,\u201d Econometrica Supplemental Material, 88, https:\/\/doi.org\/10.3982\/ECTA16557.","DOI":"10.3982\/ECTA16557"},{"key":"ecta200218-bib-0012","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1017\/S026646660809049X","volume":"25","author":"Cavaliere","year":"2009","journal-title":"Econometric Theory"},{"key":"ecta200218-bib-0013","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1080\/07474938.2012.690660","volume":"32","author":"Cavaliere","year":"2013","journal-title":"Econometric Reviews"},{"key":"ecta200218-bib-0014","doi-asserted-by":"crossref","first-page":"813","DOI":"10.3982\/ECTA11952","volume":"83","author":"Cavaliere","year":"2015","journal-title":"Econometrica"},{"key":"ecta200218-bib-0015","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1214\/aos\/1176350711","volume":"16","author":"Chan","year":"1988","journal-title":"The Annals of Statistics"},{"key":"ecta200218-bib-0016","volume-title":"Asymptotic Theory of Statistics and Probability","author":"DasGupta","year":"2008"},{"key":"ecta200218-bib-0017","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1093\/biomet\/asn011","volume":"95","author":"DiCiccio","year":"2008","journal-title":"Biometrika"},{"key":"ecta200218-bib-0018","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1080\/07350015.2017.1385467","volume":"37","author":"Georgiev","year":"2019","journal-title":"Journal of Business & Economic Statistics"},{"key":"ecta200218-bib-0019","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4384-7","volume-title":"The Bootstrap and Edgeworth Expansion","author":"Hall","year":"1992"},{"key":"ecta200218-bib-0020","doi-asserted-by":"crossref","first-page":"413","DOI":"10.2307\/2171789","volume":"64","author":"Hansen","year":"1996","journal-title":"Econometrica"},{"key":"ecta200218-bib-0021","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0304-4076(99)00068-8","volume":"97","author":"Hansen","year":"2000","journal-title":"Journal of Econometrics"},{"key":"ecta200218-bib-0022","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-18329-9","volume-title":"Stable Convergence and Stable Limit Theorems","author":"H\u00e4usler","year":"2015"},{"key":"ecta200218-bib-0023","volume-title":"Handbook of Econometrics 5","author":"Horowitz","year":"2001"},{"key":"ecta200218-bib-0024","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1017\/S0266466616000281","volume":"33","author":"Hounyo","year":"2017","journal-title":"Econometric Theory"},{"key":"ecta200218-bib-0025","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1016\/j.spa.2008.11.004","volume":"119","author":"Jacod","year":"2009","journal-title":"Stochastic Processes and Their Applications"},{"key":"ecta200218-bib-0026","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.3150\/14-BEJ689","volume":"22","author":"Johansen","year":"2016","journal-title":"Bernoulli"},{"key":"ecta200218-bib-0027","volume-title":"Foundations of Modern Probability","author":"Kallenberg","year":"1997"},{"key":"ecta200218-bib-0028","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-41598-7","volume-title":"Random Measures: Theory and Applications","author":"Kallenberg","year":"2017"},{"key":"ecta200218-bib-0029","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1214\/aos\/1176347262","volume":"17","author":"Knight","year":"1989","journal-title":"The Annals of Statistics"},{"key":"ecta200218-bib-0030","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/PL00008798","volume":"121","author":"Lahiri","year":"2001","journal-title":"Probability Theory & Related Fields"},{"key":"ecta200218-bib-0031","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/jmva.1996.0025","volume":"57","author":"LePage","year":"1996","journal-title":"Journal of Multivariate Analysis"},{"key":"ecta200218-bib-0032","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s004400050110","volume":"108","author":"LePage","year":"1997","journal-title":"Probability Theory & Related Fields"},{"key":"ecta200218-bib-0033","first-page":"349","volume":"34","author":"Linde","year":"1989","journal-title":"Theory of Probability and Its Applications"},{"key":"ecta200218-bib-0034","doi-asserted-by":"crossref","first-page":"857","DOI":"10.3150\/11-BEJ366","volume":"18","author":"Lockhart","year":"2012","journal-title":"Bernoulli"},{"key":"ecta200218-bib-0035","doi-asserted-by":"crossref","first-page":"271","DOI":"10.2307\/2951597","volume":"60","author":"Ploberger","year":"1992","journal-title":"Econometrica"},{"key":"ecta200218-bib-0036","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1554-7","volume-title":"Subsampling","author":"Politis","year":"1999"},{"key":"ecta200218-bib-0037","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1214\/ss\/1177010027","volume":"10","author":"Reid","year":"1995","journal-title":"Statistical Science"},{"key":"ecta200218-bib-0038","volume-title":"Convergence in Ergodic Theory and Probability","author":"Rubshtein","year":"1996"},{"key":"ecta200218-bib-0039","doi-asserted-by":"crossref","first-page":"1953","DOI":"10.1214\/09-AOS777","volume":"38","author":"Sen","year":"2010","journal-title":"The Annals of Statistics"},{"key":"ecta200218-bib-0040","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1111\/j.1467-9868.2012.01037.x","volume":"75","author":"Shao","year":"2013","journal-title":"Journal of the Royal Statistical Society B"},{"key":"ecta200218-bib-0041","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/BF01051878","volume":"2","author":"Sweeting","year":"1989","journal-title":"Journal of Theoretical Probability"},{"key":"ecta200218-bib-0042","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1214\/12-AOS1010","volume":"40","author":"Zhang","year":"2012","journal-title":"The Annals of Statistics"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T13:51:51Z","timestamp":1605621111000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA16557"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":42,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020]]}},"alternative-id":["10.3982\/ECTA16557"],"URL":"https:\/\/doi.org\/10.3982\/ecta16557","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2020]]}}}