{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T16:08:34Z","timestamp":1781626114857,"version":"3.54.5"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T00:00:00Z","timestamp":1766534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T00:00:00Z","timestamp":1766534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008899","name":"University of South Carolina","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008899","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Sparse linear regression methods for high-dimensional data commonly assume that errors have constant variance, which can be violated in practice. For example, Aphasia Quotient (AQ) is a critical measure of language impairment and informs treatment decisions, but it is challenging to measure in stroke patients. It is of interest to use high-resolution T2 neuroimages of brain damage to predict AQ. However, sparse regression models show marked evidence of heteroscedastic error even after transformations are applied. This violation of the homoscedasticity assumption can lead to biased and inconsistent standard errors of estimated coefficients and prediction intervals (PI) with improper length. Bayesian heteroscedastic linear regression models relax the homoscedastic error assumption but can enforce restrictive prior assumptions on parameters, and many are computationally infeasible in the high-dimensional setting. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization (H-PROBE) algorithm. H-PROBE is a computationally efficient maximum\n                    <jats:italic>a posteriori<\/jats:italic>\n                    estimation approach that requires minimal prior assumptions and can incorporate covariates known or hypothesized to impact heterogeneity. We apply this method by using high-dimensional neuroimages to predict and provide PIs for AQ that accurately quantify predictive uncertainty. Our analysis demonstrates that H-PROBE can provide narrower PI widths than standard methods without sacrificing coverage. Narrower PIs are clinically important for determining the risk of moderate to severe aphasia. Additionally, through extensive simulation studies, we exhibit that H-PROBE results in superior prediction, variable selection, and predictive inference compared to alternative methods.\n                  <\/jats:p>","DOI":"10.1007\/s00180-025-01699-y","type":"journal-article","created":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T17:17:49Z","timestamp":1766596669000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression"],"prefix":"10.1007","volume":"41","author":[{"given":"Anja","family":"Zgodic","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7190-7844","authenticated-orcid":false,"given":"Ray","family":"Bai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4566-0822","authenticated-orcid":false,"given":"Jiajia","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0685-2550","authenticated-orcid":false,"given":"Yuan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7554-6142","authenticated-orcid":false,"given":"Christopher","family":"Rorden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5475-0670","authenticated-orcid":false,"given":"Alexander C.","family":"McLain","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,12,24]]},"reference":[{"issue":"1","key":"1699_CR1","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1214\/12-AOAS575","volume":"7","author":"A Alfons","year":"2013","unstructured":"Alfons A, Croux C, Gelper S (2013) Sparse least trimmed squares regression for analyzing high-dimensional large data sets. Ann Appl Stat 7(1):226\u2013248","journal-title":"Ann Appl Stat"},{"issue":"537","key":"1699_CR2","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1080\/01621459.2020.1765784","volume":"117","author":"R Bai","year":"2022","unstructured":"Bai R, Moran GE, Antonelli JL, Boland MR (2022) Spike-and-slab group lassos for grouped regressions and sparse generalized additive models. J Am Stat Assoc 117(537):184\u2013197","journal-title":"J Am Stat Assoc"},{"key":"1699_CR3","doi-asserted-by":"publisher","first-page":"2996","DOI":"10.1038\/s41591-023-02562-7","volume":"29","author":"C Banerji","year":"2023","unstructured":"Banerji C, Chakraborti T, Harbron C, MacArthur B (2023) Clinical ai tools must convey predictive uncertainty for each individual patient. Nat Med 29:2996\u20132998","journal-title":"Nat Med"},{"key":"1699_CR4","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1038\/s42256-018-0004-1","volume":"1","author":"E Begoli","year":"2019","unstructured":"Begoli E, Bhattacharya T, Kusnezov D (2019) The need for uncertainty quantification in machine-assisted medical decision making. Nat Mach Intell 1:20\u201323","journal-title":"Nat Mach Intell"},{"issue":"2","key":"1699_CR5","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1214\/14-AOS1204","volume":"42","author":"A Belloni","year":"2014","unstructured":"Belloni A, Chernozhukov V, Wang L (2014) Pivotal estimation via square-root LASSO in nonparametric regression. Ann Stat 42(2):757\u2013788","journal-title":"Ann Stat"},{"issue":"532","key":"1699_CR6","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1080\/01621459.2019.1677471","volume":"115","author":"J Bradley","year":"2020","unstructured":"Bradley J, Holan S, Wikle C (2020) Bayesian hierarchical models with conjugate full-conditional distributions for dependent data from the natural exponential family. J Am Stat Assoc 115(532):2037\u20132052","journal-title":"J Am Stat Assoc"},{"issue":"5","key":"1699_CR7","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.2307\/1911963","volume":"47","author":"T Breusch","year":"1979","unstructured":"Breusch T, Pagan A (1979) A simple test for heteroskedasticity and random coefficient variation. Econometrica 47(5):1287\u20131294","journal-title":"Econometrica"},{"key":"1699_CR8","doi-asserted-by":"crossref","unstructured":"Buonaccorsi JP (1995) Prediction in the presence of measurement error: general discussion and an example predicting defoliation. Biometrics, pp 1562\u20131569","DOI":"10.2307\/2533288"},{"key":"1699_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2873-3","volume-title":"Transformation and weighting in regression","author":"R Carroll","year":"1988","unstructured":"Carroll R (1988) Transformation and weighting in regression. Chapman and Hall, New York"},{"key":"1699_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2873-3","volume-title":"Transformation and weighting in regression","author":"RJ Carroll","year":"1988","unstructured":"Carroll RJ, Ruppert D (1988) Transformation and weighting in regression, vol 30. CRC Press, Boca Raton"},{"issue":"2","key":"1699_CR11","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1093\/biomet\/asq017","volume":"97","author":"CM Carvalho","year":"2010","unstructured":"Carvalho CM, Polson NG, Scott JG (2010) The horseshoe estimator for sparse signals. Biometrika 97(2):465\u2013480","journal-title":"Biometrika"},{"issue":"1","key":"1699_CR12","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/j.jeconom.2020.01.009","volume":"216","author":"HT Chiou","year":"2020","unstructured":"Chiou HT, Guo M, Ing CK (2020) Variable selection for high-dimensional regression models with time series and heteroscedastic errors. J Econom 216(1):118\u2013136. https:\/\/doi.org\/10.1016\/j.jeconom.2020.01.009","journal-title":"J Econom"},{"key":"1699_CR13","volume-title":"Visualizing data","author":"W Cleveland","year":"1993","unstructured":"Cleveland W (1993) Visualizing data. Hobart Press, Offenburg"},{"issue":"4","key":"1699_CR14","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s11156-010-0212-1","volume":"37","author":"J Curto","year":"2011","unstructured":"Curto J, Pinto J, Morais A, Lourenco I (2011) The heteroskedasticity- consistent covariance estimator in accounting. Rev Quant Financ Acc 37(4):427\u2013449","journal-title":"Rev Quant Financ Acc"},{"issue":"1","key":"1699_CR15","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1111\/j.1541-0420.2011.01652.x","volume":"68","author":"ZJ Daye","year":"2012","unstructured":"Daye ZJ, Chen J, Li H (2012) High-dimensional heteroscedastic regression with an application to eQTL data analysis. Biometrics 68(1):316\u2013326. https:\/\/doi.org\/10.1111\/j.1541-0420.2011.01652.x","journal-title":"Biometrics"},{"issue":"1","key":"1699_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B Methodol 39(1):1\u201338 (With discussion)","journal-title":"J R Stat Soc Ser B Methodol"},{"issue":"1","key":"1699_CR17","first-page":"1","volume":"23","author":"B Efron","year":"2008","unstructured":"Efron B (2008) Microarrays, empirical bayes and the two-group model. Stat Sci 23(1):1\u201322","journal-title":"Stat Sci"},{"key":"1699_CR18","unstructured":"Eicker F (1967) Limit theorems for regression with unequal and dependent errors. In: Proceedings of the fifth Berkeley Symposium on mathematical statistics and probability. Vol.\u00a05, pp. 59\u201382"},{"key":"1699_CR19","volume-title":"Modelling extremal events: for insurance and finance","author":"P Embrechts","year":"2013","unstructured":"Embrechts P, Kl\u00fcppelberg C, Mikosch T (2013) Modelling extremal events: for insurance and finance, vol 33. Springer Science & Business Media, Berlin"},{"key":"1699_CR20","volume-title":"Practical methods of optimization","author":"R Fletcher","year":"1987","unstructured":"Fletcher R (1987) Practical methods of optimization. Wiley, New York"},{"issue":"20","key":"1699_CR21","doi-asserted-by":"publisher","first-page":"3899","DOI":"10.1002\/sim.9483","volume":"41","author":"B Guo","year":"2022","unstructured":"Guo B, Jaeger BC, Rahman AKMF, Long DL, Yi N (2022) Spike-and-slab least absolute shrinkage and selection operator generalized additive models and scalable algorithms for high-dimensional data analysis. Stat Med 41(20):3899\u20133914","journal-title":"Stat Med"},{"key":"1699_CR22","unstructured":"Huber P (1967) The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the fifth Berkeley Symposium on mathematical statistics and probability. Vol.\u00a05, pp. 221\u2013233"},{"key":"1699_CR23","unstructured":"Jaakkola T, Qi Y (2006) Parameter expanded variational Bayesian methods. Adv Neural Inf Process Syst 19"},{"issue":"2","key":"1699_CR24","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1044\/2018_AJSLP-18-0123","volume":"28","author":"L Johnson","year":"2019","unstructured":"Johnson L, Basilakos A, Yourganov G, Cai B, Bonilha L, Rorden C, Fridriksson J (2019) Progression of aphasia severity in the chronic stages of stroke. Am J Speech Lang Pathol 28(2):639\u2013649","journal-title":"Am J Speech Lang Pathol"},{"key":"1699_CR25","volume-title":"Western aphasia battery-revised (wab-r)","author":"A Kertesz","year":"2007","unstructured":"Kertesz A (2007) Western aphasia battery-revised (wab-r). Pearson, London"},{"issue":"3","key":"1699_CR26","doi-asserted-by":"publisher","first-page":"304","DOI":"10.3390\/brainsci11030304","volume":"11","author":"J Lee","year":"2021","unstructured":"Lee J, Ko M, Park S, Kim G (2021) Prediction of aphasia severity in patients with stroke using diffusion tensor imaging. Brain Sci 11(3):304","journal-title":"Brain Sci"},{"issue":"523","key":"1699_CR27","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1080\/01621459.2017.1307116","volume":"113","author":"J Lei","year":"2018","unstructured":"Lei J, G\u2019Sell M, Rinaldo A, Tibshirani RJ, Wasserman L (2018) Distribution-free predictive inference for regression. J Am Stat Assoc 113(523):1094\u20131111","journal-title":"J Am Stat Assoc"},{"issue":"481","key":"1699_CR28","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1198\/016214507000001337","volume":"103","author":"F Liang","year":"2008","unstructured":"Liang F, Paulo R, Molina G, Clyde MA, Berger JO (2008) Mixtures of g priors for Bayesian variable selection. J Am Stat Assoc 103(481):410\u2013423","journal-title":"J Am Stat Assoc"},{"issue":"4","key":"1699_CR29","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1093\/biomet\/85.4.755","volume":"85","author":"C Liu","year":"1998","unstructured":"Liu C, Rubin DB, Wu YN (1998) Parameter expansion to accelerate EM: the PX-EM algorithm. Biometrika 85(4):755\u2013770. https:\/\/doi.org\/10.1093\/biomet\/85.4.755","journal-title":"Biometrika"},{"key":"1699_CR30","first-page":"1","volume":"21","author":"R Martin","year":"2020","unstructured":"Martin R, Tang Y (2020) Empirical priors for prediction in sparse high-dimensional linear regression. J Mach Learn Res 21:1\u201330","journal-title":"J Mach Learn Res"},{"key":"1699_CR31","unstructured":"McLain AC, Zgodic A (2021) Fitting high-dimensional linear regression models with probe. Retrieved from https:\/\/github.com\/alexmclain\/UNHIDEM"},{"key":"1699_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2025.108146","volume":"207","author":"AC McLain","year":"2025","unstructured":"McLain AC, Zgodic A, Bondell H (2025) Sparse high-dimensional linear regression with a partitioned empirical bayes ECM algorithm. Comput Stat Data Anal 207:108146","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"1699_CR33","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1093\/biomet\/80.2.267","volume":"80","author":"XL Meng","year":"1993","unstructured":"Meng XL, Rubin DB (1993) Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80(2):267\u2013278. https:\/\/doi.org\/10.1093\/biomet\/80.2.267","journal-title":"Biometrika"},{"issue":"3","key":"1699_CR34","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1016\/j.neuroimage.2007.10.002","volume":"39","author":"P Nachev","year":"2008","unstructured":"Nachev P, Coulthard E, J\u00e4ger HR, Kennard C, Husain M (2008) Enantiomorphic normalization of focally lesioned brains. Neuroimage 39(3):1215\u20131226","journal-title":"Neuroimage"},{"issue":"4","key":"1699_CR35","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1044\/1058-0360(2005\/032)","volume":"14","author":"A Odekar","year":"2005","unstructured":"Odekar A, Hallowell B (2005) Comparison of alternatives to multidimensional scoring in the assessment of language comprehension in aphasia. Am J Speech Lang Pathol 14(4):337\u2013345. https:\/\/doi.org\/10.1044\/1058-0360(2005\/032)","journal-title":"Am J Speech Lang Pathol"},{"issue":"15","key":"1699_CR36","doi-asserted-by":"publisher","first-page":"3207","DOI":"10.1080\/00949655.2021.1925279","volume":"91","author":"P Parker","year":"2021","unstructured":"Parker P, Holan S, Wills S (2021) A general Bayesian model for heteroskedastic data with fully conjugate full-conditional distributions. J Stat Comput Simul 91(15):3207\u20133227","journal-title":"J Stat Comput Simul"},{"key":"1699_CR37","doi-asserted-by":"crossref","unstructured":"Peng P, Chiou H, Huang H, Ing C (2025) Variable selection for high-dimensional heteroscedastic regression and its applications. J Comput Graph Stat, 1\u201311","DOI":"10.1080\/10618600.2025.2450449"},{"issue":"2","key":"1699_CR38","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1080\/10618600.2019.1677243","volume":"29","author":"MT Pratola","year":"2020","unstructured":"Pratola MT, Chipman HA, George EI, McCulloch RE (2020) Heteroscedastic BART via multiplicative regression trees. J Comput Graph Stat 29(2):405\u2013417","journal-title":"J Comput Graph Stat"},{"issue":"4","key":"1699_CR39","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1080\/01688638508401277","volume":"7","author":"AH Risser","year":"1985","unstructured":"Risser AH, Spreen O (1985) The western aphasia battery. J Clin Exp Neuropsychol 7(4):463\u2013470","journal-title":"J Clin Exp Neuropsychol"},{"issue":"4","key":"1699_CR40","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1016\/j.neuroimage.2012.03.020","volume":"61","author":"C Rorden","year":"2012","unstructured":"Rorden C, Bonilha L, Fridriksson J, Bender B, Karnath H-O (2012) Age-specific CT and MRI templates for spatial normalization. Neuroimage 61(4):957\u2013965","journal-title":"Neuroimage"},{"issue":"1","key":"1699_CR41","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10618-005-0024-4","volume":"12","author":"P Rousseeuw","year":"2006","unstructured":"Rousseeuw P, Van Driessen K (2006) Computing LTS regression for large data sets. Data Min Knowl Disc 12(1):29\u201345","journal-title":"Data Min Knowl Disc"},{"key":"1699_CR42","doi-asserted-by":"crossref","unstructured":"Schlather M, Malinowski A, Menck PJ, Oesting M, Strokorb K (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. J Stat Softw 63(8):1\u201325. Retrieved from https:\/\/www.jstatsoft.org\/v63\/i08\/","DOI":"10.18637\/jss.v063.i08"},{"key":"1699_CR43","doi-asserted-by":"publisher","DOI":"10.1002\/9780471722199","volume-title":"Linear regression analysis","author":"GA Seber","year":"2003","unstructured":"Seber GA, Lee AJ (2003) Linear regression analysis, vol 330. Wiley, New York"},{"issue":"4","key":"1699_CR44","doi-asserted-by":"publisher","first-page":"836","DOI":"10.1198\/106186002871","volume":"11","author":"G Smyth","year":"2002","unstructured":"Smyth G (2002) An efficient algorithm for Reml in heteroscedastic regression. J Comput Graph Stat 11(4):836\u2013847","journal-title":"J Comput Graph Stat"},{"key":"1699_CR45","unstructured":"Tang Y, Martin R (2021) Vienna, Austria. Retrieved from https:\/\/CRAN.R-project.org\/package=ebreg (R package version 0.1.3)"},{"key":"1699_CR46","doi-asserted-by":"crossref","unstructured":"Teghipco A, Newman-Norlund R, Fridriksson J, Rorden C, Bonilha L (2023) Distinct brain morphometry patterns revealed by deep learning improve prediction of aphasia severity. Res Sq","DOI":"10.21203\/rs.3.rs-3126126\/v1"},{"key":"1699_CR47","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1023\/A:1018917218956","volume":"12","author":"V Temlyakov","year":"2000","unstructured":"Temlyakov V (2000) Weak greedy algorithms. Adv Comput Math 12:213\u2013227","journal-title":"Adv Comput Math"},{"key":"1699_CR48","unstructured":"Tibshirani R, Foygel R (2019) Conformal prediction under covariate shift. Adv Neural Inf Process Syst"},{"key":"1699_CR49","volume-title":"Algorithmic learning in a random world","author":"V Vovk","year":"2005","unstructured":"Vovk V, Gammerman A, Shafer G (2005) Algorithmic learning in a random world. Springer Science & Business Media, Berlin"},{"key":"1699_CR51","doi-asserted-by":"crossref","unstructured":"Wang X, Leng C (2016) High dimensional ordinary least squares projection for screening variables. J R Stat Soc Ser B (Stat Methodol) 78(3):589\u2013611. Retrieved from 2022-10-08 http:\/\/www.jstor.org\/stable\/24775353","DOI":"10.1111\/rssb.12127"},{"issue":"3","key":"1699_CR50","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1198\/073500106000000251","volume":"25","author":"H Wang","year":"2007","unstructured":"Wang H, Li G, Jiang G (2007) Robust regression shrinkage and consistent variable selection through the LAD-Lasso. J Bus Econ Stat 25(3):347\u2013355. https:\/\/doi.org\/10.1198\/073500106000000251","journal-title":"J Bus Econ Stat"},{"issue":"4","key":"1699_CR52","doi-asserted-by":"publisher","first-page":"817","DOI":"10.2307\/1912934","volume":"48","author":"H White","year":"1980","unstructured":"White H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817\u2013838","journal-title":"Econometrica"},{"key":"1699_CR53","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.cortex.2015.09.005","volume":"73","author":"G Yourganov","year":"2015","unstructured":"Yourganov G, Smith K, Fridriksson J, Rorden C (2015) Predicting aphasia type from brain damage measured with structural mri. Cortex 73:203\u20132015","journal-title":"Cortex"},{"key":"1699_CR55","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2021.1970570","author":"L Zhou","year":"2021","unstructured":"Zhou L, Zou H (2021) Cross-fitted residual regression for high-dimensional heteroscedasticity pursuit. J Am Stat Assoc. https:\/\/doi.org\/10.1080\/01621459.2021.1970570","journal-title":"J Am Stat Assoc"},{"key":"1699_CR54","unstructured":"Zhou K, Li K-C, Zhou Q (2021) Honest confidence sets for high-dimensional regression by projection and shrinkage. J Am Statist Assoc, pp 1\u201320"},{"key":"1699_CR56","doi-asserted-by":"publisher","unstructured":"Ziel F (2016) Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes. Comput Stat Data Anal 100:773\u2013793. Retrieved from https:\/\/doi.org\/10.1016\/j.csda.2015.11.016.  arxiv:1502.06557","DOI":"10.1016\/j.csda.2015.11.016"},{"issue":"1","key":"1699_CR57","doi-asserted-by":"publisher","DOI":"10.1016\/j.metrad.2023.100003","volume":"1","author":"K Zou","year":"2023","unstructured":"Zou K, Chen Z, Yuan X, Shen X, Wang M, Fu H (2023) A review of uncertainty estimation and its application in medical imaging. Meta-Radiology 1(1):100003","journal-title":"Meta-Radiology"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01699-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-025-01699-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01699-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T15:46:21Z","timestamp":1781624781000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-025-01699-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,24]]},"references-count":57,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1699"],"URL":"https:\/\/doi.org\/10.1007\/s00180-025-01699-y","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,24]]},"assertion":[{"value":"1 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no Conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval and consent to participate"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"7"}}