{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T01:07:04Z","timestamp":1779930424044,"version":"3.53.1"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T00:00:00Z","timestamp":1777852800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000155","name":"Social Sciences and Humanities Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics & Data Analysis"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.csda.2026.108400","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T07:04:41Z","timestamp":1777964681000},"page":"108400","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Adaptive robust estimation for varying coefficient models"],"prefix":"10.1016","volume":"222","author":[{"given":"Tao","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weixin","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0001","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11749-013-0346-2","article-title":"P-splines quantile regression estimation in varying coefficient models","volume":"23","author":"Andriyana","year":"2014","journal-title":"TEST"},{"key":"10.1016\/j.csda.2026.108400_bib0002","first-page":"1","article-title":"Posterior concentration rates for Bayesian penalized splines","author":"Bach","year":"2025","journal-title":"Bayesian Anal."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0003","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1002\/cjs.11661","article-title":"Robust estimation and variable selection for function-on-scalar regression","volume":"50","author":"Cai","year":"2022","journal-title":"Can. J. Stat."},{"issue":"451","key":"10.1016\/j.csda.2026.108400_bib0004","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1080\/01621459.2000.10474280","article-title":"Efficient estimation and inferences for varying-coefficient models","volume":"95","author":"Cai","year":"2000","journal-title":"J. Am. Stat. Assoc."},{"issue":"451","key":"10.1016\/j.csda.2026.108400_bib0005","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1080\/01621459.2000.10474284","article-title":"Functional-coefficient regression models for nonlinear time series","volume":"95","author":"Cai","year":"2000","journal-title":"J. Am. Stat. Assoc."},{"issue":"490","key":"10.1016\/j.csda.2026.108400_bib0006","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1198\/jasa.2010.tm08636","article-title":"Global partial likelihood for nonparametric proportional hazards models","volume":"105","author":"Chen","year":"2010","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10.1016\/j.csda.2026.108400_bib0007","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1093\/biomet\/asr081","article-title":"Efficient estimation for the cox model with varying coefficients","volume":"99","author":"Chen","year":"2012","journal-title":"Biometrika"},{"issue":"2","key":"10.1016\/j.csda.2026.108400_bib0008","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1080\/07474938.2024.2410765","article-title":"Regularized maximum likelihood estimation for the random coefficients model","volume":"44","author":"Dunker","year":"2025","journal-title":"Econom. Rev."},{"key":"10.1016\/j.csda.2026.108400_bib0009","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.3150\/bj\/1137421639","article-title":"Profile likelihood inferences on semiparametric varying coefficient partially linear models","volume":"11","author":"Fan","year":"2005","journal-title":"Bernoulli"},{"issue":"5","key":"10.1016\/j.csda.2026.108400_bib0010","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1214\/aos\/1017939139","article-title":"Statistical estimation in varying coefficient models","volume":"27","author":"Fan","year":"1999","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2026.108400_bib0011","doi-asserted-by":"crossref","first-page":"179","DOI":"10.4310\/SII.2008.v1.n1.a15","article-title":"Statistical methods with varying coefficient models","volume":"1","author":"Fan","year":"2008","journal-title":"Stat. Interface"},{"key":"10.1016\/j.csda.2026.108400_bib0012","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1214\/23-EJS2117","article-title":"Variable selection for single-index varying-coefficients models with applications to synergistic g\u202f\u00d7\u202fe interactions","volume":"17","author":"Guan","year":"2023","journal-title":"Electron. J. Stat."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0013","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0095-0696(78)90006-2","article-title":"Hedonic housing prices and the demand for clean air","volume":"5","author":"Harrison","year":"1978","journal-title":"J. Environ. Econ. Manag."},{"issue":"4","key":"10.1016\/j.csda.2026.108400_bib0014","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1111\/j.2517-6161.1993.tb01939.x","article-title":"Varying-coefficient models","volume":"55","author":"Hastie","year":"1993","journal-title":"J. R. Stat. Soc. B"},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0015","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0378-3758(03)00110-1","article-title":"Quantile regression in varying coefficient models","volume":"121","author":"Honda","year":"2004","journal-title":"J. Stat. Plan. Inference"},{"issue":"4","key":"10.1016\/j.csda.2026.108400_bib0016","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1093\/biomet\/85.4.809","article-title":"Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data","volume":"85","author":"Hoover","year":"1998","journal-title":"Biometrika"},{"issue":"8","key":"10.1016\/j.csda.2026.108400_bib0017","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1080\/00949655.2022.2135708","article-title":"Generalized varying-coefficient additive model for locally stationary time series","volume":"93","author":"Hu","year":"2023","journal-title":"J. Stat. Comput. Simul."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0018","first-page":"763","article-title":"Polynomial spline estimation and inference for varying coefficient models with longitudinal data","volume":"14","author":"Huang","year":"2004","journal-title":"Stat. Sin."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0019","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1093\/restud\/rdr043","article-title":"Optimal bandwidth choice for the regression discontinuity estimator","volume":"79","author":"Imbens","year":"2012","journal-title":"Rev. Econ. Stud."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0020","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.csda.2004.05.006","article-title":"Penalized spline smoothing in multivariable survival models with varying coefficients","volume":"49","author":"Kauermann","year":"2005","journal-title":"Comput. Stat. Data Anal."},{"issue":"26","key":"10.1016\/j.csda.2026.108400_bib0021","doi-asserted-by":"crossref","first-page":"4764","DOI":"10.1002\/sim.7034","article-title":"Semi-varying coefficient multinomial logistic regression for disease progression risk prediction","volume":"35","author":"Ke","year":"2016","journal-title":"Stat. Med."},{"issue":"551","key":"10.1016\/j.csda.2026.108400_bib0022","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1080\/01621459.2025.2480867","article-title":"Estimation and inference of quantile spatially varying coefficient models over complicated domains","volume":"120","author":"Kim","year":"2025","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0023","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1214\/009053606000000966","article-title":"Quantile regression with varying coefficients","volume":"35","author":"Kim","year":"2007","journal-title":"Ann. Stat."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0024","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s00184-025-01008-z","article-title":"Partially linear varying-coefficient quantile regression with truncated and missing data","volume":"89","author":"Kong","year":"2026","journal-title":"Metrika"},{"issue":"4","key":"10.1016\/j.csda.2026.108400_bib0025","doi-asserted-by":"crossref","first-page":"1618","DOI":"10.1214\/15-AOS1430","article-title":"Estimation of semi-varying coefficient time series models with arma errors","volume":"44","author":"Lei","year":"2016","journal-title":"Ann. Stat."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0026","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1111\/sjos.12196","article-title":"A semiparametrically efficient estimator of the time-varying effects for survival data with time-dependent treatment","volume":"43","author":"Lin","year":"2016","journal-title":"Scand. J. Stat."},{"key":"10.1016\/j.csda.2026.108400_bib0027","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jspi.2015.08.002","article-title":"A global partial likelihood estimation in the additive cox proportional hazards model","volume":"169","author":"Lin","year":"2016","journal-title":"J. Stat. Plan. Inference"},{"key":"10.1016\/j.csda.2026.108400_bib0028","first-page":"847","article-title":"Efficient estimation and computation in generalized varying coefficient models with unknown link and variance functions for large-scale data","volume":"32","author":"Lin","year":"2022","journal-title":"Stat. Sin."},{"key":"10.1016\/j.csda.2026.108400_bib0029","first-page":"779","article-title":"A semiparametrically efficient estimator of single-index varying coefficient cox proportional hazards models","volume":"26","author":"Lin","year":"2016","journal-title":"Stat. Sin."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0030","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1002\/cjs.11510","article-title":"Global kernel estimator and test of varying-coefficient autoregressive model","volume":"47","author":"Lin","year":"2019","journal-title":"Can. J. Stat."},{"issue":"2","key":"10.1016\/j.csda.2026.108400_bib0031","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1080\/10618600.2024.2403705","article-title":"Bootstrap inference for linear time-varying coefficient models in locally stationary time series","volume":"34","author":"Lin","year":"2025","journal-title":"J. Comput. Graph. Stat."},{"key":"10.1016\/j.csda.2026.108400_bib0032","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.jmva.2013.08.007","article-title":"A robust and efficient estimation method for single index models","volume":"122","author":"Liu","year":"2013","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2026.108400_bib0033","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.csda.2014.08.006","article-title":"An efficient and robust variable selection method for longitudinal generalized linear models","volume":"82","author":"Lv","year":"2015","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0034","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1111\/insr.12029","article-title":"Varying coefficient regression models: a review and new developments","volume":"83","author":"Park","year":"2015","journal-title":"Int. Stat. Rev."},{"issue":"424","key":"10.1016\/j.csda.2026.108400_bib0035","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1080\/01621459.1993.10476408","article-title":"Alternatives to the median absolute deviation","volume":"88","author":"Rousseeuw","year":"1993","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108400_bib0036","doi-asserted-by":"crossref","DOI":"10.1016\/j.csda.2020.107094","article-title":"Robust variable selection with exponential squared loss for the spatial autoregressive model","volume":"155","author":"Song","year":"2021","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.csda.2026.108400_bib0037","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jspi.2016.01.006","article-title":"Robust structure identification and variable selection in partial linear varying coefficient models","volume":"174","author":"Wang","year":"2016","journal-title":"J. Stat. Plan. Inference"},{"key":"10.1016\/j.csda.2026.108400_bib0038","first-page":"2617","article-title":"Derivative estimation based on difference sequence via locally weighted least squares regression","volume":"16","author":"Wang","year":"2015","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"10.1016\/j.csda.2026.108400_bib0039","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1080\/10618600.2023.2267616","article-title":"Varying coefficient model via adaptive spline fitting","volume":"33","author":"Wang","year":"2024","journal-title":"J. Comput. Graph. Stat."},{"issue":"502","key":"10.1016\/j.csda.2026.108400_bib0040","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1080\/01621459.2013.766613","article-title":"Robust variable selection with exponential squared loss","volume":"108","author":"Wang","year":"2013","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108400_bib0041","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s10463-023-00870-w","article-title":"Robust variable selection with exponential squared loss for partially linear spatial autoregressive models","volume":"75","author":"Wang","year":"2023","journal-title":"Ann. Inst. Stat. Math."},{"issue":"444","key":"10.1016\/j.csda.2026.108400_bib0042","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1080\/01621459.1998.10473800","article-title":"Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data","volume":"93","author":"Wu","year":"1998","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108400_bib0043","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1007\/s00180-023-01372-2","article-title":"Empirical likelihood and estimation in varying coefficient models with right censored data","volume":"39","author":"Xue","year":"2024","journal-title":"Comput. Stat."},{"issue":"550","key":"10.1016\/j.csda.2026.108400_bib0044","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1080\/01621459.2024.2359131","article-title":"Distributed heterogeneity learning for generalized partially linear models with spatially varying coefficients","volume":"120","author":"Yu","year":"2025","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108400_bib0045","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1006\/jmva.1999.1883","article-title":"Variable bandwidth selection in varying-coefficient models","volume":"74","author":"Zhang","year":"2000","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2026.108400_bib0046","doi-asserted-by":"crossref","DOI":"10.1016\/j.csda.2023.107808","article-title":"The Bayesian regularized quantile varying coefficient model","volume":"187","author":"Zhou","year":"2023","journal-title":"Comput. Stat. Data Anal."},{"issue":"3","key":"10.1016\/j.csda.2026.108400_bib0047","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1111\/sjos.12717","article-title":"Empirical likelihood M-estimation for the varying-coefficient model with functional response","volume":"51","author":"Zhou","year":"2024","journal-title":"Scand. J. Stat."}],"container-title":["Computational Statistics & Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326000691?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326000691?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T00:46:08Z","timestamp":1779929168000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947326000691"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":47,"alternative-id":["S0167947326000691"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2026.108400","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Adaptive robust estimation for varying coefficient models","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2026.108400","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"108400"}}