{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T01:25:47Z","timestamp":1772933147873,"version":"3.50.1"},"reference-count":58,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1612891"],"award-info":[{"award-number":["1612891"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1,506,879"],"award-info":[{"award-number":["DMS 1,506,879"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Spain Ministry of Science and Innovation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002924","name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002924","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MCIN \/ AEI \/10.13039\/50-1100011033"],"award-info":[{"award-number":["MCIN \/ AEI \/10.13039\/50-1100011033"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["PID2022-138268NB-I00"],"award-info":[{"award-number":["PID2022-138268NB-I00"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007406","name":"Fundaci\u00f3n BBVA","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007406","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008562","name":"University of Texas at Austin","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008562","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006375","name":"Universit\u00e0 Bocconi","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006375","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":[[2026,3]]},"DOI":"10.1016\/j.csda.2025.108275","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T11:40:56Z","timestamp":1758022856000},"page":"108275","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Recursive nonparametric predictive for a discrete regression model"],"prefix":"10.1016","volume":"215","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6682-908X","authenticated-orcid":false,"given":"Lorenzo","family":"Cappello","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen G.","family":"Walker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.csda.2025.108275_bib0001","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1093\/biomet\/63.3.413","article-title":"Multivariate binary discrimination by the kernel method","volume":"63","author":"Aitchison","year":"1976","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2025.108275_bib0002","series-title":"Ecole d\u2019Ete de Probabilites de Saint-Flour","first-page":"1","article-title":"Exchangeability and related topics","author":"Aldous","year":"1985"},{"key":"10.1016\/j.csda.2025.108275_bib0003","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1080\/01621459.2013.879061","article-title":"A Bayesian nonparametric regression model with normalized weights: a study of hippocampal atrophy in Alzheimer\u2019s disease","volume":"109","author":"Antoniano-Villalobos","year":"2014","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2025.108275_bib0004","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1214\/009117904000000676","article-title":"Limit theorems for a class of identically distributed random variables","volume":"32","author":"Berti","year":"2004","journal-title":"Ann. Probab."},{"key":"10.1016\/j.csda.2025.108275_bib0005","series-title":"Convergence of Probability Measures","author":"Billingsley","year":"2013"},{"key":"10.1016\/j.csda.2025.108275_bib0006","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1214\/aoms\/1177728659","article-title":"Multidimensional stochastic approximation methods","volume":"25","author":"Blum","year":"1954","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0007","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/s11009-017-9587-y","article-title":"A Bayesian motivated Laplace inversion for multivariate probability distributions","volume":"20","author":"Cappello","year":"2018","journal-title":"Methodol. Comput. Appl. Probab."},{"key":"10.1016\/j.csda.2025.108275_bib0008","article-title":"Recursive estimation of probability distributions","author":"Cappello","year":"2025","journal-title":"submitted"},{"key":"10.1016\/j.csda.2025.108275_bib0009","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1198\/016214504000000205","article-title":"An ANOVA model for dependent random measures","volume":"99","author":"De Iorio","year":"2004","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2025.108275_bib0010","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1214\/15-AOS1391","article-title":"Nonparametric stochastic approximation with large step-sizes","volume":"44","author":"Dieuleveut","year":"2016","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0011","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1093\/biomet\/asn012","article-title":"Kernel stick-breaking processes","volume":"95","author":"Dunson","year":"2008","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2025.108275_bib0012","doi-asserted-by":"crossref","first-page":"2504","DOI":"10.1214\/009053607000000253","article-title":"Conditional density estimation in a regression setting","volume":"35","author":"Efromovich","year":"2007","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0013","series-title":"Technical Report","article-title":"Computing Bayesian Nonparametric Hierarchical Models","author":"Escobar","year":"1992"},{"key":"10.1016\/j.csda.2025.108275_bib0014","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1214\/aos\/1176342360","article-title":"A Bayesian analysis of some nonparametric problems","volume":"1","author":"Ferguson","year":"1973","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0015","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1093\/jrsssb\/qkad005","article-title":"Martingale posterior distributions","volume":"85","author":"Fong","year":"2023","journal-title":"J. Royal Stat. Soc. Series B"},{"key":"10.1016\/j.csda.2025.108275_bib0016","unstructured":"Fong, E., Yiu, A., 2024. Asymptotics for parametric martingale posteriors. arXiv preprint arXiv: 2410.17692."},{"issue":"1","key":"10.1016\/j.csda.2025.108275_bib0017","first-page":"86","article-title":"Exchangeability, predictive distributions and parametric models","volume":"62","author":"Fortini","year":"2000","journal-title":"Sankhy\u0101: Ind. J. Stat. Ser. A"},{"issue":"3","key":"10.1016\/j.csda.2025.108275_bib0018","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/j.spa.2017.06.008","article-title":"On a notion of partially conditionally identically distributed sequences","volume":"128","author":"Fortini","year":"2018","journal-title":"Stoch. Process. Their Appl."},{"issue":"4","key":"10.1016\/j.csda.2025.108275_bib0019","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1111\/rssb.12385","article-title":"Quasi-Bayes properties of a procedure for sequential learning in mixture models","volume":"82","author":"Fortini","year":"2020","journal-title":"J. Royal Stat. Soc. Ser. B"},{"key":"10.1016\/j.csda.2025.108275_bib0020","series-title":"Fundamentals of Nonparametric Bayesian Inference","volume":"Vol. 44","author":"Ghosal","year":"2017"},{"key":"10.1016\/j.csda.2025.108275_bib0021","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.jeconom.2011.03.001","article-title":"Stick-breaking autoregressive processes","volume":"162","author":"Griffin","year":"2011","journal-title":"J. Econom."},{"key":"10.1016\/j.csda.2025.108275_bib0022","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1080\/01621459.2017.1304219","article-title":"On recursive predictive distributions","volume":"113","author":"Hahn","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2025.108275_bib0023","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1080\/01621459.1992.10476257","article-title":"Kernel regression when the boundary region is large, with an application to testing the adequacy of polynomial models","volume":"87","author":"Hart","year":"1992","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2025.108275_bib0024","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v027.i05","article-title":"Nonparametric econometrics: the NP package","volume":"27","author":"Hayfield","year":"2008","journal-title":"J. Stat. Softw."},{"key":"10.1016\/j.csda.2025.108275_bib0025","series-title":"Bayesian Nonparametrics","volume":"Vol. 28","author":"Hjort","year":"2010"},{"key":"10.1016\/j.csda.2025.108275_bib0026","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1017\/S1748499518000039","article-title":"Real-time Bayesian nonparametric prediction of solvency risk","volume":"13","author":"Hong","year":"2019","journal-title":"Ann. Actuarial Sci."},{"key":"10.1016\/j.csda.2025.108275_bib0027","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1136\/jcp.36.10.1193","article-title":"Serum immunoglobulin concentrations in preschool children measured by laser nephelometry: reference ranges for IGG, IGA, IGM","volume":"36","author":"Isaacs","year":"1983","journal-title":"J. Clin. Pathol."},{"key":"10.1016\/j.csda.2025.108275_bib0028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v040.i05","article-title":"DPPackage: Bayesian semi-and nonparametric modeling in R","volume":"40","author":"Jara","year":"2011","journal-title":"J. Stat. Softw."},{"key":"10.1016\/j.csda.2025.108275_bib0029","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1214\/aoms\/1177729392","article-title":"Stochastic estimation of the maximum of a regression function","volume":"23","author":"Kiefer","year":"1952","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0030","series-title":"Stochastic Approximation and Recursive Algorithms and Applications","volume":"Vol. 35","author":"Kushner","year":"2003"},{"key":"10.1016\/j.csda.2025.108275_bib0031","series-title":"Stochastic Approximation Methods for Constrained and Unconstrained Systems","author":"Kushner","year":"1978"},{"key":"10.1016\/j.csda.2025.108275_bib0032","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1214\/aos\/1051027873","article-title":"Stochastic approximation","volume":"31","author":"Lai","year":"2003","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0033","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/S0047-259X(02)00025-8","article-title":"Nonparametric estimation of distributions with categorical and continuous data","volume":"86","author":"Li","year":"2003","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2025.108275_bib0034","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1214\/aos\/1176346412","article-title":"On a class of Bayesian nonparametric estimates: I. density estimates","volume":"12","author":"Lo","year":"1984","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0035","series-title":"ASA Proceedings of the Section on Bayesian Statistical Science","first-page":"50","article-title":"Dependent nonparametric processes","author":"MacEachern","year":"1999"},{"key":"10.1016\/j.csda.2025.108275_bib0036","series-title":"Technical Report","article-title":"Dependent Dirichlet Pxrocesses","author":"MacEachern","year":"2000"},{"key":"10.1016\/j.csda.2025.108275_bib0037","series-title":"Fast Nonparametric Estimation of Mixing Distributions with Application to High-Fimensional Inference","author":"Martin","year":"2009"},{"key":"10.1016\/j.csda.2025.108275_bib0038","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1214\/08-STS265","article-title":"Stochastic approximation and Newton\u2019s estimate of a mixing distribution","volume":"23","author":"Martin","year":"2008","journal-title":"Stat. Sci."},{"key":"10.1016\/j.csda.2025.108275_bib0039","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1214\/09-EJS458","article-title":"Asymptotic properties of predictive recursion: robustness and rate of convergence","volume":"3","author":"Martin","year":"2009","journal-title":"Electron. J. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0040","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1093\/biomet\/asr030","article-title":"Semiparametric inference in mixture models with predictive recursion marginal likelihood","volume":"98","author":"Martin","year":"2011","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2025.108275_bib0041","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1214\/009053606000001451","article-title":"A companion for the Kiefer\u2013Wolfowitz\u2013Blum stochastic approximation algorithm","volume":"35","author":"Mokkadem","year":"2007","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0042","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1111\/j.1467-9876.2005.05475.x","article-title":"A nonparametric Bayesian model for inference in related longitudinal studies","volume":"54","author":"M\u00fcller","year":"2005","journal-title":"J. Royal Stat. Soc. Ser. C"},{"key":"10.1016\/j.csda.2025.108275_bib0043","series-title":"An Introduction to Copulas","author":"Nelsen","year":"2007"},{"key":"10.1016\/j.csda.2025.108275_bib0044","series-title":"Practical Nonparametric and Semiparametric Bayesian Statistics","first-page":"45","article-title":"Nonparametric Bayes methods using predictive updating","author":"Newton","year":"1998"},{"key":"10.1016\/j.csda.2025.108275_bib0045","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1093\/biomet\/86.1.15","article-title":"A recursive algorithm for nonparametric analysis with missing data","volume":"86","author":"Newton","year":"1999","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2025.108275_bib0046","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1137\/0330046","article-title":"Acceleration of stochastic approximation by averaging","volume":"30","author":"Polyak","year":"1992","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.csda.2025.108275_bib0047","first-page":"391","article-title":"Robbins-Monro procedure in a Hilbert space and its application in the theory of learning processes I","volume":"8","author":"R\u00e9v\u00e9sz","year":"1973","journal-title":"Studia Scientiarum Mathematicarum Hungarica"},{"key":"10.1016\/j.csda.2025.108275_bib0048","first-page":"119","article-title":"How to apply the method of stochastic approximation in the non-parametric estimation of a regression function 1","volume":"8","author":"R\u00e9v\u00e9sz","year":"1977","journal-title":"Statistics"},{"key":"10.1016\/j.csda.2025.108275_bib0049","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1214\/aoms\/1177729586","article-title":"A stochastic approximation method","volume":"22","author":"Robbins","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0050","series-title":"Optimizing Methods in Statistics","first-page":"233","article-title":"A convergence theorem for non negative almost supermartingales and some applications","author":"Robbins","year":"1971"},{"key":"10.1016\/j.csda.2025.108275_bib0051","first-page":"145","article-title":"Nonparametric Bayesian models through probit stick-breaking processes","volume":"6","author":"Rodriguez","year":"2011","journal-title":"Bayesian Anal."},{"key":"10.1016\/j.csda.2025.108275_bib0052","first-page":"461","article-title":"Efficient recursive estimation; application to estimating the parameters of a covariance function","volume":"3","author":"Sakrison","year":"1965","journal-title":"Int. J. Eng. Sci."},{"key":"10.1016\/j.csda.2025.108275_bib0053","first-page":"639","article-title":"A constructive definition of Dirichlet priors","volume":"4","author":"Sethuraman","year":"1994","journal-title":"Stat. Sin."},{"key":"10.1016\/j.csda.2025.108275_bib0054","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1111\/j.2517-6161.1978.tb01654.x","article-title":"A quasi-Bayes sequential procedure for mixtures","volume":"40","author":"Smith","year":"1978","journal-title":"J. Royal Stat. Soc. Ser. B"},{"key":"10.1016\/j.csda.2025.108275_bib0055","doi-asserted-by":"crossref","first-page":"2502","DOI":"10.1214\/08-AOS639","article-title":"Consistency of a recursive estimate of mixing distributions","volume":"37","author":"Tokdar","year":"2009","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2025.108275_bib0056","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s11222-016-9631-8","article-title":"A Laplace transform inversion method for probability distribution functions","volume":"27","author":"Walker","year":"2017","journal-title":"Stat. Comput."},{"key":"10.1016\/j.csda.2025.108275_bib0057","doi-asserted-by":"crossref","first-page":"5113","DOI":"10.1080\/03610918.2016.1144766","article-title":"An iterative algorithm for solving sparse linear equations","volume":"46","author":"Walker","year":"2017","journal-title":"Commun. Stat. Simul. Comput."},{"key":"10.1016\/j.csda.2025.108275_bib0058","first-page":"1","article-title":"Bayesian nonparametric clustering for large data sets","volume":"to appear","author":"Zuanetti","year":"2018","journal-title":"Stat. Comput."}],"container-title":["Computational Statistics &amp; Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947325001513?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947325001513?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T06:30:08Z","timestamp":1772865008000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947325001513"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3]]},"references-count":58,"alternative-id":["S0167947325001513"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2025.108275","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Recursive nonparametric predictive for a discrete regression model","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2025.108275","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Authors. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"108275"}}