{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T14:00:44Z","timestamp":1785074444561,"version":"3.55.0"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100010031","name":"Postdoctoral Research Foundation of China","doi-asserted-by":"publisher","award":["2024M752706"],"award-info":[{"award-number":["2024M752706"]}],"id":[{"id":"10.13039\/501100010031","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010023","name":"Natural Science Research of Jiangsu Higher Education Institutions of China","doi-asserted-by":"publisher","award":["24KJB110030"],"award-info":[{"award-number":["24KJB110030"]}],"id":[{"id":"10.13039\/501100010023","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018529","name":"Major Project of Philosophy and Social Science Research in Colleges and Universities of Jiangsu Province","doi-asserted-by":"publisher","award":["2024SJYB1531"],"award-info":[{"award-number":["2024SJYB1531"]}],"id":[{"id":"10.13039\/501100018529","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12501357"],"award-info":[{"award-number":["12501357"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401380"],"award-info":[{"award-number":["12401380"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics &amp; Data Analysis"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.csda.2026.108417","type":"journal-article","created":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T23:12:43Z","timestamp":1779750763000},"page":"108417","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Distributed quantile regression via convolution smoothing and optimal subsampling"],"prefix":"10.1016","volume":"224","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4295-502X","authenticated-orcid":false,"given":"Jun","family":"Jin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinhan","family":"Liang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tiefeng","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuangzhe","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.csda.2026.108417_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.jco.2020.101512","article-title":"Optimal subsampling for large-scale quantile regression","volume":"62","author":"Ai","year":"2021","journal-title":"J. Complex."},{"issue":"2","key":"10.1016\/j.csda.2026.108417_bib0002","first-page":"749","article-title":"Optimal subsampling algorithms for big data regressions","volume":"31","author":"Ai","year":"2021","journal-title":"Stat. Sin."},{"issue":"3","key":"10.1016\/j.csda.2026.108417_bib0003","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1214\/17-AOS1587","article-title":"Distributed testing and estimation under sparse high dimensional models","volume":"46","author":"Battey","year":"2018","journal-title":"Ann. Stat."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0004","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1080\/10618600.2025.2513964","article-title":"Communication-efficient pilot estimation for non-randomly distributed data in diverging dimensions","volume":"35","author":"Chao","year":"2026","journal-title":"J. Comput. Graph. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0005","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1093\/jrsssb\/qkaf017","article-title":"Multi-resolution subsampling for linear classification with massive data","volume":"87","author":"Chen","year":"2025","journal-title":"J. R. Stat. Soc. B: Stat. Methodol."},{"issue":"6","key":"10.1016\/j.csda.2026.108417_bib0006","doi-asserted-by":"crossref","first-page":"3244","DOI":"10.1214\/18-AOS1777","article-title":"Quantile regression under memory constraint","volume":"47","author":"Chen","year":"2019","journal-title":"Ann. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0007","first-page":"1655","article-title":"A split-and-conquer approach for analysis of extraordinarily large data","volume":"24","author":"Chen","year":"2014","journal-title":"Stat. Sin."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0008","first-page":"3475","article-title":"Fast approximation of matrix coherence and statistical leverage","volume":"13","author":"Drineas","year":"2012","journal-title":"J. Mach. Learn. Res."},{"issue":"542","key":"10.1016\/j.csda.2026.108417_bib0009","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1080\/01621459.2021.1969238","article-title":"Communication-efficient accurate statistical estimation","volume":"118","author":"Fan","year":"2023","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10.1016\/j.csda.2026.108417_bib0010","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1214\/17-AOS1568","article-title":"I-LAMM for sparse learning: simultaneous control of algorithmic complexity and statistical error","volume":"46","author":"Fan","year":"2018","journal-title":"Ann. Stat."},{"issue":"2","key":"10.1016\/j.csda.2026.108417_bib0011","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1007\/s00180-022-01318-0","article-title":"Distributed quantile regression for longitudinal big data","volume":"39","author":"Fan","year":"2024","journal-title":"Comput. Stat."},{"key":"10.1016\/j.csda.2026.108417_bib0012","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.ins.2023.02.065","article-title":"Communication-efficient distributed estimation of partially linear additive models for large-scale data","volume":"631","author":"Gao","year":"2023","journal-title":"Inf. Sci."},{"issue":"2","key":"10.1016\/j.csda.2026.108417_bib0013","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jeconom.2021.07.010","article-title":"Smoothed quantile regression with large-scale inference","volume":"232","author":"He","year":"2023","journal-title":"J. Econom."},{"key":"10.1016\/j.csda.2026.108417_bib0014","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neucom.2021.03.041","article-title":"Distributed quantile regression for massive heterogeneous data","volume":"448","author":"Hu","year":"2021","journal-title":"Neurocomputing"},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0015","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s10107-019-01369-0","article-title":"A distributed one-step estimator","volume":"174","author":"Huang","year":"2019","journal-title":"Math. Program."},{"key":"10.1016\/j.csda.2026.108417_bib0016","series-title":"Advances in Neural Information Processing Systems","first-page":"3068","article-title":"Communication-efficient distributed dual coordinate ascent","volume":"Vol. 27","author":"Jaggi","year":"2014"},{"key":"10.1016\/j.csda.2026.108417_bib0017","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.neucom.2021.08.101","article-title":"Smoothing quantile regression for a distributed system","volume":"466","author":"Jiang","year":"2021","journal-title":"Neurocomputing"},{"issue":"526","key":"10.1016\/j.csda.2026.108417_bib0018","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1080\/01621459.2018.1429274","article-title":"Communication-efficient distributed statistical inference","volume":"114","author":"Jordan","year":"2019","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0019","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.jmva.2004.05.006","article-title":"Quantile regression for longitudinal data","volume":"91","author":"Koenker","year":"2004","journal-title":"J. Multivar. Anal."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0020","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/1913643","article-title":"Regression quantiles","volume":"46","author":"Koenker","year":"1978","journal-title":"Econometrica"},{"issue":"2","key":"10.1016\/j.csda.2026.108417_bib0021","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1111\/j.1467-9469.2008.00626.x","article-title":"Bayesian semiparametric modelling in quantile regression","volume":"36","author":"Kottas","year":"2009","journal-title":"Scand. J. Stat."},{"issue":"5","key":"10.1016\/j.csda.2026.108417_bib0022","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s11222-024-10477-7","article-title":"Distributed subsampling for multiplicative regression","volume":"34","author":"Li","year":"2024","journal-title":"Stat. Comput."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0023","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s11222-024-10449-x","article-title":"Poisson subsampling-based estimation for growing-dimensional expectile regression in massive data","volume":"34","author":"Li","year":"2024","journal-title":"Stat. Comput."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0024","first-page":"861","article-title":"A statistical perspective on algorithmic leveraging","volume":"16","author":"Ma","year":"2015","journal-title":"J. Mach. Learn. Res."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0025","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1080\/07350015.2021.1961789","article-title":"A note on distributed quantile regression by pilot sampling and one-step updating","volume":"40","author":"Pan","year":"2022","journal-title":"J. Bus. Econ. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0026","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1214\/ss\/1030037960","article-title":"The Gaussian hare and the Laplacian tortoise: computability of squared-error versus absolute-error estimators","volume":"12","author":"Portnoy","year":"1997","journal-title":"Stat. Sci."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0027","first-page":"379","article-title":"On the optimality of averaging in distributed statistical learning","volume":"5","author":"Rosenblatt","year":"2016","journal-title":"Inf. Inference: J. IMA"},{"key":"10.1016\/j.csda.2026.108417_bib0028","series-title":"International Conference on Machine Learning","first-page":"1000","article-title":"Communication-efficient distributed optimization using an approximate newton-type method","author":"Shamir","year":"2014"},{"issue":"14","key":"10.1016\/j.csda.2026.108417_bib0029","doi-asserted-by":"crossref","first-page":"2719","DOI":"10.1080\/02664763.2024.2315467","article-title":"Optimal poisson subsampling decorrelated score for high-dimensional generalized linear models","volume":"51","author":"Shan","year":"2024","journal-title":"J. Appl. Stat."},{"issue":"272","key":"10.1016\/j.csda.2026.108417_bib0030","first-page":"1","article-title":"Communication-constrained distributed quantile regression with optimal statistical guarantees","volume":"23","author":"Tan","year":"2022","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0031","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1111\/rssb.12485","article-title":"High-dimensional quantile regression: convolution smoothing and concave regularization","volume":"84","author":"Tan","year":"2022","journal-title":"J. R. Stat. Soc. B: Stat. Methodol."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0032","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1093\/biomet\/asaa043","article-title":"Optimal subsampling for quantile regression in big data","volume":"108","author":"Wang","year":"2021","journal-title":"Biometrika"},{"issue":"525","key":"10.1016\/j.csda.2026.108417_bib0033","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1080\/01621459.2017.1408468","article-title":"Information-based optimal subdata selection for big data linear regression","volume":"114","author":"Wang","year":"2019","journal-title":"J. Am. Stat. Assoc."},{"issue":"522","key":"10.1016\/j.csda.2026.108417_bib0034","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1080\/01621459.2017.1292914","article-title":"Optimal subsampling for large sample logistic regression","volume":"113","author":"Wang","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108417_bib0035","series-title":"International Conference on Machine Learning","first-page":"3636","article-title":"Efficient distributed learning with sparsity","author":"Wang","year":"2017"},{"key":"10.1016\/j.csda.2026.108417_bib0036","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2022.119418","article-title":"Smooth quantile regression and distributed inference for non-randomly stored big data","volume":"215","author":"Wang","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.csda.2026.108417_bib0037","doi-asserted-by":"crossref","DOI":"10.1016\/j.csda.2021.107225","article-title":"Robust distributed modal regression for massive data","volume":"160","author":"Wang","year":"2021","journal-title":"Comput. Stat. Data Anal."},{"issue":"3","key":"10.1016\/j.csda.2026.108417_bib0038","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s11222-023-10247-x","article-title":"Distributed statistical optimization for non-randomly stored big data with application to penalized learning","volume":"33","author":"Wang","year":"2023","journal-title":"Stat. Comput."},{"key":"10.1016\/j.csda.2026.108417_bib0039","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2022.116698","article-title":"Efficient statistical estimation for a non-randomly distributed system with application to large-scale data neural network","volume":"197","author":"Wang","year":"2022","journal-title":"Expert Syst. Appl."},{"issue":"6","key":"10.1016\/j.csda.2026.108417_bib0040","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1142\/S0219530520500098","article-title":"Communication-efficient estimation of high-dimensional quantile regression","volume":"18","author":"Wang","year":"2020","journal-title":"Anal. Appl."},{"key":"10.1016\/j.csda.2026.108417_bib0041","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.eswa.2017.01.054","article-title":"Composite quantile regression neural network with applications","volume":"76","author":"Xu","year":"2017","journal-title":"Expert Syst. Appl."},{"issue":"537","key":"10.1016\/j.csda.2026.108417_bib0042","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1080\/01621459.2020.1773832","article-title":"Optimal distributed subsampling for maximum quasi-likelihood estimators with massive data","volume":"117","author":"Yu","year":"2022","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2026.108417_bib0043","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1080\/10618600.2024.2421990","article-title":"Optimal subsampling for data streams with measurement constrained categorical responses","volume":"34","author":"Yu","year":"2025","journal-title":"J. Comput. Graph. Stat."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0044","first-page":"3299","article-title":"Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates","volume":"16","author":"Zhang","year":"2015","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"10.1016\/j.csda.2026.108417_bib0045","first-page":"3321","article-title":"Communication-efficient algorithms for statistical optimization","volume":"14","author":"Zhang","year":"2013","journal-title":"J. Mach. Learn. Res."},{"issue":"4","key":"10.1016\/j.csda.2026.108417_bib0046","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1080\/10618600.2021.1923517","article-title":"Least-square approximation for a distributed system","volume":"30","author":"Zhu","year":"2021","journal-title":"J. Comput. Graph. Stat."},{"issue":"476","key":"10.1016\/j.csda.2026.108417_bib0047","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The adaptive lasso and its oracle properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Computational Statistics &amp; Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326000861?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326000861?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T13:17:24Z","timestamp":1785071844000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947326000861"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":47,"alternative-id":["S0167947326000861"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2026.108417","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Distributed quantile regression via convolution smoothing and optimal subsampling","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2026.108417","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108417"}}