{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T06:22:00Z","timestamp":1791181320630,"version":"4.1.0"},"reference-count":99,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T00:00:00Z","timestamp":1334188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Prediction and estimation based on Bayesian model selection and model averaging, and derived methods such as the Bayesian information criterion BIC, do not always converge at the fastest possible rate. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods, which inspires a modification of the Bayesian predictive distribution, called the switch distribution. When used as an adaptive estimator, the switch distribution does achieve optimal cumulative risk convergence rates in non-parametric density estimation and Gaussian regression problems. We show that the minimax cumulative risk is obtained under very weak conditions and without knowledge of the underlying degree of smoothness. Unlike other adaptive model selection procedures such as the Akaike information criterion AIC and leave-one-out cross-validation, BIC and Bayes factor model selection are typically statistically consistent. We show that this property is retained by the switch distribution, which thus solves the AIC\u2013BIC dilemma for cumulative risk. The switch distribution has an efficient implementation. We compare its performance with AIC, BIC and Bayesian model selection and averaging on a regression problem with simulated data.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2011.01025.x","type":"journal-article","created":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T20:02:21Z","timestamp":1334260941000},"page":"361-417","source":"Crossref","is-referenced-by-count":54,"title":["Catching up Faster by Switching Sooner: A Predictive Approach to Adaptive Estimation with an Application to the AIC\u2013BIC Dilemma"],"prefix":"10.1093","volume":"74","author":[{"given":"Tim","family":"Van Erven","sequence":"first","affiliation":[{"name":"Centrum voor Wiskunde en Informatica , Amsterdam , The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Gr\u00fcnwald","sequence":"additional","affiliation":[{"name":"Centrum voor Wiskunde en Informatica , Amsterdam , The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven","family":"de Rooij","sequence":"additional","affiliation":[{"name":"Centrum voor Wiskunde en Informatica , Amsterdam , The Netherlands"},{"name":"University of Cambridge , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2012,4,12]]},"reference":[{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1093\/biomet\/66.2.237","article-title":"A Bayesian extension of the minimum AIC procedure of autoregressive model fitting","volume":"66","author":"Akaike","year":"1979","journal-title":"Biometrika"},{"key":"2023031108552123000_","first-page":"27","volume-title":"Bayesian Statistics 6","author":"Barron","year":"1998"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1109\/18.86996","article-title":"Minimum complexity density estimation","volume":"37","author":"Barron","year":"1991","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"2743","DOI":"10.1109\/18.720554","article-title":"The minimum description length principle in coding and modeling","volume":"44","author":"Barron","year":"1998","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","first-page":"1347","article-title":"Approximation of density functions by sequences of exponential families","volume":"19","author":"Barron","year":"1991","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","first-page":"38","volume-title":"Proc. Int. Symp. Information Theory, Trondheim","author":"Barron","year":"1994"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316870","volume-title":"Bayesian Theory","author":"Bernardo","year":"1994"},{"key":"2023031108552123000_","volume-title":"Bayesian Inference in Statistical Analysis","author":"Box","year":"1973"},{"key":"2023031108552123000_","volume-title":"Model Selection and Multimodel Inference","author":"Burnham","year":"2002"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546921","volume-title":"Prediction, Learning and Games","author":"Cesa-Bianchi","year":"2006"},{"key":"2023031108552123000_","volume-title":"Technical Report","author":"Clarke","year":"1997"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1109\/18.54897","article-title":"Information-theoretic asymptotics of Bayes methods","volume":"36","author":"Clarke","year":"1990","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0378-3758(94)90153-8","article-title":"Jeffreys\u2019 prior is asymptotically least favorable under entropy risk","volume":"41","author":"Clarke","year":"1994","journal-title":"J. Statist. Planng Inf."},{"key":"2023031108552123000_","first-page":"278","article-title":"Statistical theory: the prequential approach","volume":"147","author":"Dawid","year":"1984","journal-title":"J. R. Statist. Soc."},{"key":"2023031108552123000_","first-page":"109","volume-title":"Bayesian Statistics","author":"Dawid","year":"1992"},{"key":"2023031108552123000_","first-page":"113","volume-title":"Current Issues in Statistical Inference: Essays in Honor of D. Basu","author":"Dawid","year":"1992"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1111\/1467-9469.00321","article-title":"Choosing a model selection strategy","volume":"30","author":"De Luna","year":"2003","journal-title":"Scand. J. Statist."},{"key":"2023031108552123000_","first-page":"1","article-title":"On the consistency of Bayes estimates","volume":"14","author":"Diaconis","year":"1986","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/81.3.425","article-title":"Ideal spatial adaptation by wavelet shrinkage","volume":"81","author":"Donoho","year":"1994","journal-title":"Biometrika"},{"key":"2023031108552123000_","volume-title":"PhD Thesis","author":"van Erven","year":"2010"},{"key":"2023031108552123000_","volume-title":"Preprint arXiv:0807.1005","author":"van Erven","year":"2008"},{"key":"2023031108552123000_","first-page":"83","volume-title":"Simplicity, Inference and Modelling","author":"Forster","year":"2001"},{"key":"2023031108552123000_","first-page":"1947","article-title":"The risk inflation criterion for multiple regression","volume":"22","author":"Forster","year":"1994","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1214\/07-EJS090","article-title":"Nonparametric Bayesian model selection and averaging","volume":"2","author":"Ghosal","year":"2008","journal-title":"Electron. J. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4643.001.0001","volume-title":"The Minimum Description Length Principle","author":"Gr\u00fcwald","year":"2007"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1198\/016214501753168398","article-title":"Model selection and the principle of minimum description length","volume":"96","author":"Hansen","year":"2001","journal-title":"J. Am. Statist. Ass."},{"key":"2023031108552123000_","volume-title":"Science and Statistics: Festschrift for Terry Speed","author":"Hansen","year":"2002"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1214\/aos\/1030741081","article-title":"Mutual information, metric entropy and cumulative relative entropy risk","volume":"25","author":"Haussler","year":"1997","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1023\/A:1007424614876","article-title":"Tracking the best expert","volume":"32","author":"Herbster","year":"1998","journal-title":"Mach. Learn."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/01621459.1995.10476572","article-title":"Bayes factors","volume":"90","author":"Kass","year":"1995","journal-title":"J. Am. Statist. Ass."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1023\/A:1008984400380","article-title":"On predictive distributions and Bayesian networks","volume":"10","author":"Kontkanen","year":"2000","journal-title":"J. Statist. Comput."},{"key":"2023031108552123000_","article-title":"Combining expert advice efficiently","author":"Koolen","year":"2008","journal-title":"Proc. 21st A. Conf. Computational Learning Theorey"},{"key":"2023031108552123000_","article-title":"Combining expert advice efficiently","author":"Koolen","year":"2008","journal-title":"Preprint arXiv abs\/0802.2015"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1214\/aos\/1176350486","article-title":"Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation: discrete index set","volume":"15","author":"Li","year":"1987","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"3780","DOI":"10.1109\/TIT.2005.856956","article-title":"Asymptotics of discrete MDL for online prediction","volume":"51","author":"Poland","year":"2005","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/TIT.1984.1056936","article-title":"Universal coding, information, prediction, and estimation","volume":"30","author":"Rissanen","year":"1984","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1109\/18.119689","article-title":"Density estimation by stochastic complexity","volume":"38","author":"Rissanen","year":"1992","journal-title":"IEEE Trans. Inform. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/BF02480998","article-title":"Asymptotic mean efficiency of a selection of regression variables","volume":"35","author":"Shibata","year":"1983","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2539-1","volume-title":"Probability","author":"Shiryaev","year":"1996"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1080\/10635150490468657","article-title":"The contest between parsimony and likelihood","volume":"4","author":"Sober","year":"2004","journal-title":"Syst. Biol."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF00773667","article-title":"Model selection and prediction: normal regression","volume":"45","author":"Speed","year":"1993","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1111\/j.2517-6161.1977.tb01603.x","article-title":"An asymptotic equivalence of choice of model by cross-validation and Akaike\u2019s criterion","volume":"39","author":"Stone","year":"1977","journal-title":"J. R. Statist. Soc."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Statist. Soc."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/DCC.1998.672217","article-title":"Switching between two universal source coding algoriths","author":"Volf","year":"1998","journal-title":"Proc. Data Compression Con., Snowbird"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1023\/A:1007595032382","article-title":"Derandomizing stochastic prediction strategies","volume":"35","author":"Vovk","year":"1999","journal-title":"Mach. Learn."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2307\/3315929","article-title":"Improvement over Bayes prediction in small samples in the presence of model uncertainty","volume":"32","author":"Wong","year":"2004","journal-title":"Can. J. Statist."},{"key":"2023031108552123000_","first-page":"475","article-title":"Model selection for nonparametric regression","volume":"9","author":"Yang","year":"1999","journal-title":"Statist. Sin."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1214\/aos\/1016120365","article-title":"Mixing strategies for density estimation","volume":"28","author":"Yang","year":"2000","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1093\/biomet\/92.4.937","article-title":"Can the strengths of AIC and BIC be shared","volume":"92","author":"Yang","year":"2005","journal-title":"Biometrika"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1214\/009053607000000514","article-title":"Consistency of cross-validation for comparing regression procedures","volume":"35","author":"Yang","year":"2007","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","first-page":"1","article-title":"Prediction estimation with simple linear models: is it really that simple?","volume":"23","author":"Yang","year":"2007","journal-title":"Econmetr. Theor."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1214\/aos\/1017939142","article-title":"Information-theoretic determination of minimax rates of convergence","volume":"27","author":"Yang","year":"1999","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1111\/j.2517-6161.1991.tb01812.x","article-title":"Posterior Bayes factors (with discussion)","volume":"53","author":"Aitkin","year":"1991","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0165-0270(00)00344-7","article-title":"Construction and analysis of non-Poisson stimulus-response models of neural spiking activity","volume":"105","author":"Barbieri","year":"2001","journal-title":"J. Neursci. Meth."},{"key":"2023031108552123000_","article-title":"Estimating space and space-time covariance functions for large data sets: a weighted composite likelihood approach","author":"Bevilacqua","year":"2011","journal-title":"J. Am. Statist. Ass."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF02294361","article-title":"Model selection and Akaike\u2019s information criterion (AIC): the general theory and its analytical extensions","volume":"52","author":"Bozdogan","year":"1987","journal-title":"Psychometrika"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"7411","DOI":"10.1523\/JNEUROSCI.18-18-07411.1998","article-title":"A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells","volume":"18","author":"Brown","year":"1998","journal-title":"J. Neursci."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546921","volume-title":"Prediction, Learning, and Games","author":"Cesa-Bianchi","year":"2006"},{"key":"2023031108552123000_","volume-title":"Technical Report TR-10-98","author":"Chen","year":"1998"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/978-3-642-04414-4_6","volume-title":"Proc. 20th Int. Conf. Algorithmic Learning Theory","author":"Chernov","year":"2009"},{"key":"2023031108552123000_","volume-title":"SMC2: a sequential Monte Carlo algorithm with particle Markov chain Monte Carlo updates","author":"Chopin","year":"2011"},{"key":"2023031108552123000_","volume-title":"Model Selection and Model Averaging","author":"Claeskens","year":"2008"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1002\/sam.10052","article-title":"Prequential analysis of complex data with adaptive model reselection","volume":"2","author":"Clarke","year":"2009","journal-title":"Statist. Anal. Data Min."},{"key":"2023031108552123000_","first-page":"604","article-title":"The well-calibrated Bayesian (with discussion)","volume":"77","author":"Dawid","year":"1982","journal-title":"J. Am. Statist. Ass."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"278","DOI":"10.2307\/2981683","article-title":"Statistical theory: the prequential approach (with discussion)","volume":"147","author":"Dawid","year":"1984","journal-title":"J. R. Statist. Soc. A"},{"key":"2023031108552123000_","first-page":"210","volume-title":"Encyclopedia of Statistical Sciences","author":"Dawid","year":"1986"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1111\/j.2517-6161.1991.tb01810.x","article-title":"Fisherian inference in likelihood and prequential frames of reference (with discussion)","volume":"53","author":"Dawid","year":"1991","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","first-page":"113","volume-title":"Current Issues in Statistical Inference: Essays in Honor of D. Basu","author":"Dawid","year":"1992"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1093\/oso\/9780198522669.003.0007","volume-title":"Bayesian Statistics 4","author":"Dawid","year":"1992"},{"key":"2023031108552123000_","first-page":"464","volume-title":"Encyclopedia of Statistical Sciences","author":"Dawid","year":"1997"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"125","DOI":"10.2307\/3318616","article-title":"Prequential probability: principles and properties","volume":"5","author":"Dawid","year":"1999","journal-title":"Bernoulli"},{"key":"2023031108552123000_","volume-title":"Calibration results for Bayesian model specification","author":"Draper","year":"2011"},{"key":"2023031108552123000_","first-page":"334","volume-title":"Proc. 29th A. Symp. Theory of Computing","author":"Freund","year":"1997"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","DOI":"10.1201\/9780429258480","volume-title":"Bayesian Data Analysis","author":"Gelman","year":"2003"},{"key":"2023031108552123000_","first-page":"459","article-title":"Interpolating between types and tokens by estimating power law generators","volume":"18","author":"Goldwater","year":"2006","journal-title":"Adv. Neur. Inform. Process. Syst."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1111\/j.2517-6161.1979.tb01072.x","article-title":"The determination of the order of an autoregression","volume":"41","author":"Hannan","year":"1979","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","first-page":"1238","volume":"35","author":"Ing C.-K. (2007) Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","first-page":"41","article-title":"A consistent and bias corrected extension of Akaike\u2019s information criterion (AIC): AICbc(k)","volume":"2","author":"Kwon","year":"1998","journal-title":"J. Kor. Soc. Industrl Appl. Math."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"2074","DOI":"10.1214\/11-AOS899","article-title":"Parametric or nonparametric?: a parametricness index for model selection","volume":"39","author":"Liu","year":"2011","journal-title":"Ann. Statist."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0167-7152(88)90050-8","article-title":"Canonical kernels for density estimation","volume":"7","author":"Marron","year":"1988","journal-title":"Statist. Probab. Lett."},{"key":"2023031108552123000_","volume-title":"Technical Report 0108","author":"Neal","year":"2001"},{"key":"2023031108552123000_","first-page":"294","article-title":"Occam\u2019s razor","volume":"13","author":"Rasmussen","year":"2001","journal-title":"Adv. Neur. Inform. Process. Syst."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jmp.2005.11.008","article-title":"An empirical study of minimum description length model selection with infinite parametric complexity","volume":"50","author":"de Rooij","year":"2006","journal-title":"J. Math. Psychol."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1111\/j.1467-9868.2008.00700.x","article-title":"Approxiamate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion)","volume":"71","author":"Rue","year":"2009","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","volume-title":"Density Estimation for Statistics and Data Analysis","author":"Silverman","year":"1986"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0304-4076(94)01701-8","article-title":"Information criteria for selecting possibly misspecified parametric models","volume":"71","author":"Sin","year":"1996","journal-title":"J. Econmetr."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1093\/biomet\/86.4.765","article-title":"On efficient probability forecasting systems","volume":"86","author":"Skouras","year":"1999","journal-title":"Biometrika"},{"key":"2023031108552123000_","volume-title":"Research Report 218","author":"Skouras","year":"2000"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF00773667","article-title":"Model selection and prediction: normal regression","volume":"45","author":"Speed","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1111\/1467-9868.00353","article-title":"Bayesian measures of model complexity and fit (with discussion)","volume":"64","author":"Spiegelhalter","year":"2002","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1111\/j.2517-6161.1979.tb01084.x","article-title":"Comments on model selection criteria of Akaike and Schwartz","volume":"41","author":"Stone","year":"1979","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031108552123000_","first-page":"985","article-title":"A hierarchical Bayesian language model based on Pitman-Yor processes","author":"Teh","year":"2006","journal-title":"Proc. 21st Int. Conf. Computational Linguistics and 44th A. Meet. Association for Computational Linguistics"},{"key":"2023031108552123000_","volume-title":"Master\u2019s Thesis","author":"Van Ommen","year":"2011"},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1023\/A:1007595032382","article-title":"Derandomizing stochastic prediction strategies","volume":"35","author":"Vovk","journal-title":"Mach. Learn."},{"key":"2023031108552123000_","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1111\/j.1751-5823.2001.tb00457.x","article-title":"Competitive on-line statistics","volume":"69","author":"Vovk","year":"2001","journal-title":"Int. Statist. Rev."},{"key":"2023031108552123000_","first-page":"937","article-title":"Can the strengths of AIC and BIC be shared?","volume":"92","author":"Yang","year":"2005","journal-title":"J. Am. Statist. Ass."},{"key":"2023031108552123000_","first-page":"1","article-title":"Prediction estimation with simple linear models: is it really that simple?","volume":"23","author":"Yang","year":"2007","journal-title":"Econmetr. Theor."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2011.01025.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/74\/3\/361\/49509529\/jrsssb_74_3_361.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/74\/3\/361\/49509529\/jrsssb_74_3_361.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T04:27:47Z","timestamp":1713846467000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/74\/3\/361\/7075307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,12]]},"references-count":99,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,4,12]]},"published-print":{"date-parts":[[2012,6,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2011.01025.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2012,6]]},"published":{"date-parts":[[2012,4,12]]}}}