{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:47:51Z","timestamp":1759146471765,"version":"3.37.3"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T00:00:00Z","timestamp":1604102400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T00:00:00Z","timestamp":1604102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771240"],"award-info":[{"award-number":["11771240"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s00180-020-01043-6","type":"journal-article","created":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T12:02:42Z","timestamp":1604145762000},"page":"1197-1218","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Simultaneous confidence bands for comparing variance functions of two samples based on deterministic designs"],"prefix":"10.1007","volume":"36","author":[{"given":"Chen","family":"Zhong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3894-873X","authenticated-orcid":false,"given":"Lijian","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,31]]},"reference":[{"key":"1043_CR1","first-page":"65","volume":"2","author":"S Bose","year":"1935","unstructured":"Bose S, Mahalanobis P (1935) On the distribution of the ratio of variances of two samples drawn from a given normal bivariate correlated population. Sankhy\u0101 Indian J Stat 2:65\u201372","journal-title":"Sankhy\u0101 Indian J Stat"},{"key":"1043_CR2","first-page":"1852","volume":"31","author":"P Bickel","year":"1973","unstructured":"Bickel P, Rosenblatt M (1973) On some global measures of deviations of density function estimates. Ann Stat 31:1852\u20131884","journal-title":"Ann Stat"},{"key":"1043_CR3","doi-asserted-by":"crossref","first-page":"2219","DOI":"10.1214\/009053607000000145","volume":"35","author":"L Brown","year":"2007","unstructured":"Brown L, Levine M (2007) Variance estimation in nonparametric regression via the difference sequence method. Ann Stat 35:2219\u20132232","journal-title":"Ann Stat"},{"key":"1043_CR4","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1214\/aos\/1074290329","volume":"31","author":"G Claeskens","year":"2003","unstructured":"Claeskens G, Van Keilegom I (2003) Bootstrap confidence bands for regression curves and their derivatives. Ann Stat 31:1852\u20131884","journal-title":"Ann Stat"},{"key":"1043_CR5","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1007\/s11749-015-0427-5","volume":"24","author":"L Cai","year":"2015","unstructured":"Cai L, Yang L (2015) A smooth simultaneous confidence band for conditional variance function. TEST 24:632\u2013655","journal-title":"TEST"},{"key":"1043_CR6","first-page":"505","volume":"29","author":"L Cai","year":"2019","unstructured":"Cai L, Liu R, Wang S, Yang L (2019) Simutaneous confidence bands for mean and varience functions based on deterministic design. Stat Sin 29:505\u2013525","journal-title":"Stat Sin"},{"key":"1043_CR7","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1007\/s11749-019-00655-5","volume":"29","author":"L Cai","year":"2020","unstructured":"Cai L, Li L, Huang S, Ma L, Yang L (2020) Oracally efficient estimation for dense functional data with holiday effects. TEST 29:282\u2013306","journal-title":"TEST"},{"key":"1043_CR8","first-page":"359","volume":"26","author":"G Cao","year":"2016","unstructured":"Cao G, Wang L, Li Y, Yang L (2016) Oracle-efficient confidence envelopes for covariance functions in dense functional data. Stat Sin 26:359\u2013383","journal-title":"Stat Sin"},{"key":"1043_CR9","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1080\/10485252.2011.638071","volume":"24","author":"G Cao","year":"2012","unstructured":"Cao G, Yang L, Todem D (2012) Simultaneous inference for the mean function based on dense functional data. J Nonparametr Stat 24:359\u2013377","journal-title":"J Nonparametr Stat"},{"key":"1043_CR10","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.5705\/ss.2009.207","volume":"21","author":"D Degras","year":"2011","unstructured":"Degras D (2011) Simultaneous confidence bands for nonparametric regression with functional data. Stat Sin 21:1735\u20131765","journal-title":"Stat Sin"},{"key":"1043_CR11","volume-title":"A Practical Guide to Splines","author":"C de Boor","year":"2001","unstructured":"de Boor C (2001) A Practical Guide to Splines. Springer, New York"},{"key":"1043_CR12","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1080\/01621459.1993.10476410","volume":"88","author":"R Eubank","year":"1993","unstructured":"Eubank R, Speckman P (1993) Confidence bands in nonparametric regression. J Am Stat Assoc 88:1287\u20131301","journal-title":"J Am Stat Assoc"},{"key":"1043_CR13","first-page":"190","volume":"30","author":"D Finney","year":"1938","unstructured":"Finney D (1938) The distribution of the ratio of estimates of the two variances in a sample from a normal bi-variate population. Biometrika 30:190\u2013192","journal-title":"Biometrika"},{"key":"1043_CR14","first-page":"805","volume":"2","author":"R Fisher","year":"1924","unstructured":"Fisher R (1924) On a distribution yielding the error function of several well known statistics. Proc Int Congr Math 2:805\u2013813","journal-title":"Proc Int Congr Math"},{"key":"1043_CR15","volume-title":"Local Polynomial Modelling and Its Applications","author":"J Fan","year":"1996","unstructured":"Fan J, Gijbels I (1996) Local Polynomial Modelling and Its Applications. Chapman and Hall, London"},{"key":"1043_CR16","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1093\/biomet\/37.3-4.236","volume":"37","author":"A Gayen","year":"1950","unstructured":"Gayen A (1950) The distribution of the variance ratio in random samples of any size drawn from non-normal universes. Biometrika 37:236\u2013255","journal-title":"Biometrika"},{"key":"1043_CR17","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1007\/s11749-014-0392-4","volume":"23","author":"L Gu","year":"2014","unstructured":"Gu L, Wang L, H\u00e4rdle W, Yang L (2014) A simultaneous confidence corridor for varying coefficient regression with sparse functional data. TEST 23:806\u2013843","journal-title":"TEST"},{"key":"1043_CR18","first-page":"1540","volume":"9","author":"L Gu","year":"2015","unstructured":"Gu L, Yang L (2015) Oracally efficient estimation for single-index link function with simultaneous confidence band. Electron J Stat 9:1540\u20131561","journal-title":"Electron J Stat"},{"key":"1043_CR19","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1007\/s10463-018-0668-7","volume":"71","author":"L Gu","year":"2019","unstructured":"Gu L, Wang S, Yang L (2019) Simultaneous confidence bands for the distribution function of a finite population in stratified sampling. Ann Inst Stat Math 71:983\u20131005","journal-title":"Ann Inst Stat Math"},{"key":"1043_CR20","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0047-259X(89)90022-5","volume":"29","author":"W H\u00e4rdle","year":"1989","unstructured":"H\u00e4rdle W (1989) Asmptotic maximal deviation of M-smoothers. J Multivar Anal 29:163\u2013179","journal-title":"J Multivar Anal"},{"key":"1043_CR21","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1214\/aos\/1176348120","volume":"19","author":"W H\u00e4rdle","year":"1991","unstructured":"H\u00e4rdle W, Marron J (1991) Bootstrap simultaneous error bars for nonparametric regression. Ann Stat 19:778\u2013796","journal-title":"Ann Stat"},{"key":"1043_CR22","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/0047-259X(88)90127-3","volume":"27","author":"P Hall","year":"1988","unstructured":"Hall P, Titterington D (1988) On confidence bands in nonparametric density estimation and regression. J Multivar Anal 27:228\u2013254","journal-title":"J Multivar Anal"},{"key":"1043_CR23","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1093\/biomet\/38.3-4.324","volume":"38","author":"G James","year":"1951","unstructured":"James G (1951) The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika 38:324\u2013329","journal-title":"Biometrika"},{"key":"1043_CR24","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2020.1800039","author":"J Jiang","year":"2020","unstructured":"Jiang J, Cai L, Yang L (2020) Simultaneous confidence band for the difference of regression functions of two samples. Commun Stat Theory Methods. https:\/\/doi.org\/10.1080\/03610926.2020.1800039","journal-title":"Commun Stat Theory Methods"},{"key":"1043_CR25","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/0047-259X(82)90074-4","volume":"12","author":"G Johnston","year":"1982","unstructured":"Johnston G (1982) Probabilities of maximal deviations for nonparametric regression function estimates. J Multivar Anal 12:402\u2013414","journal-title":"J Multivar Anal"},{"key":"1043_CR26","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.ijrmms.2012.09.006","volume":"58","author":"J Ju","year":"2013","unstructured":"Ju J, Xu J (2013) Structural characteristics of key strata and strata behaviour of a fully mechanized longwall face with 7.0m height chocks. Int J Rock Mech Min Sci 58:46\u201354","journal-title":"Int J Rock Mech Min Sci"},{"key":"1043_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5449-2","volume-title":"Extremes and related properties of random sequences and processes","author":"MR Leadbetter","year":"1983","unstructured":"Leadbetter MR, Lindgren G, Rootz\u00e9n H (1983) Extremes and related properties of random sequences and processes. Springer, New York"},{"key":"1043_CR28","doi-asserted-by":"crossref","first-page":"3405","DOI":"10.1016\/j.csda.2005.08.001","volume":"50","author":"M Levine","year":"2006","unstructured":"Levine M (2006) Bandwidth selection for a class of difference-based variance estimators in the nonparametric regression: a possible approach. Comput Stat Data Anal 50:3405\u20133431","journal-title":"Comput Stat Data Anal"},{"key":"1043_CR29","first-page":"95","volume":"22","author":"S Ma","year":"2012","unstructured":"Ma S, Yang L, Carroll R (2012) A simultaneous confidence band for sparse longitudinal regression. Stat Sin 22:95\u2013122","journal-title":"Stat Sin"},{"key":"1043_CR30","volume-title":"Mining pressure and strata control","author":"M Qian","year":"2010","unstructured":"Qian M, Shi P, Xu J (2010) Mining pressure and strata control. China University of Mining and Technology Press, Beijing"},{"key":"1043_CR31","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1214\/aoms\/1177731535","volume":"13","author":"H Scheff\u00e9","year":"1942","unstructured":"Scheff\u00e9 H (1942) On the ratio of the variances of two normal populations. Ann Math Stat 13:371\u2013388","journal-title":"Ann Math Stat"},{"key":"1043_CR32","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1080\/10485250902811151","volume":"5","author":"Q Song","year":"2009","unstructured":"Song Q, Yang L (2009) Spline confidence bands for variance functions. J Nonparametr Stat 5:589\u2013609","journal-title":"J Nonparametr Stat"},{"key":"1043_CR33","doi-asserted-by":"crossref","first-page":"5195","DOI":"10.1080\/03610926.2012.729643","volume":"43","author":"Q Song","year":"2014","unstructured":"Song Q, Liu R, Shao Q, Yang L (2014) A simultaneous confidence band for dense longitudinal regression. Commun Stat Theory Methods 43:5195\u20135210","journal-title":"Commun Stat Theory Methods"},{"key":"1043_CR34","first-page":"325","volume":"19","author":"J Wang","year":"2009","unstructured":"Wang J, Yang L (2009) Polynomial spline confidence bands for regression curves. Stat Sin 19:325\u2013342","journal-title":"Stat Sin"},{"key":"1043_CR35","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s10463-010-0311-8","volume":"64","author":"J Wang","year":"2012","unstructured":"Wang J (2012) Modelling time trend via spline confidence band. Ann Inst Stat Math 64:275\u2013301","journal-title":"Ann Inst Stat Math"},{"key":"1043_CR36","first-page":"654","volume":"42","author":"J Wang","year":"2014","unstructured":"Wang J, Liu R, Cheng F, Yang L (2014) Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band. Ann Stat 42:654\u2013668","journal-title":"Ann Stat"},{"key":"1043_CR37","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1007\/s11749-016-0491-5","volume":"25","author":"J Wang","year":"2016","unstructured":"Wang J, Wang S, Yang L (2016) Simultaneous confidence bands for the distribution function of a finite population and its superpopulation. TEST 25:692\u2013709","journal-title":"TEST"},{"key":"1043_CR38","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1093\/biomet\/29.3-4.350","volume":"29","author":"B Welch","year":"1938","unstructured":"Welch B (1938) The significance of the difference between two means when the population variances are unequal. Biometrika 29:350\u2013362","journal-title":"Biometrika"},{"key":"1043_CR39","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1111\/1467-9868.00155","volume":"60","author":"Y Xia","year":"1998","unstructured":"Xia Y (1998) Bias-corrected confidence bands in nonparametric regression. J R Stat Soc Ser B 60:797\u2013811","journal-title":"J R Stat Soc Ser B"},{"key":"1043_CR40","first-page":"1423","volume":"16","author":"L Xue","year":"2006","unstructured":"Xue L, Yang L (2006) Additive coefficient modeling via polynomial spline. Stat Sin 16:1423\u20131446","journal-title":"Stat Sin"},{"key":"1043_CR41","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.1214\/07-AOS533","volume":"36","author":"Z Zhao","year":"2008","unstructured":"Zhao Z, Wu W (2008) Confidence bands in nonparametric time series regression. Ann Stat 36:1854\u20131878","journal-title":"Ann Stat"},{"key":"1043_CR42","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s11749-017-0543-5","volume":"27","author":"Y Zhang","year":"2018","unstructured":"Zhang Y, Yang L (2018) A smooth simultaneous confidence band for correlation curve. TEST 27:247\u2013269","journal-title":"TEST"},{"key":"1043_CR43","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/01621459.2013.866899","volume":"109","author":"S Zheng","year":"2014","unstructured":"Zheng S, Yang L, H\u00e4rdle W (2014) A smooth simultaneous confidence corridor for the mean of sparse functional data. J Am Stat Assoc 109:661\u2013673","journal-title":"J Am Stat Assoc"},{"key":"1043_CR44","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s11749-016-0480-8","volume":"25","author":"S Zheng","year":"2016","unstructured":"Zheng S, Liu R, Yang L, H\u00e4rdle W (2016) Statistical inference for generalized additive models:simultaneous confidence corridors and variable selection. TEST 25:607\u2013626","journal-title":"TEST"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-01043-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-020-01043-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-01043-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,10]],"date-time":"2021-05-10T07:11:41Z","timestamp":1620630701000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-020-01043-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,31]]},"references-count":44,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1043"],"URL":"https:\/\/doi.org\/10.1007\/s00180-020-01043-6","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"type":"print","value":"0943-4062"},{"type":"electronic","value":"1613-9658"}],"subject":[],"published":{"date-parts":[[2020,10,31]]},"assertion":[{"value":"8 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}