{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,10]],"date-time":"2026-11-10T03:30:59Z","timestamp":1794281459468,"version":"4.9.0"},"reference-count":65,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2005,2,8]],"date-time":"2005-02-08T00:00:00Z","timestamp":1107820800000},"content-version":"unspecified","delay-in-days":7,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2005,2]]},"abstract":"<jats:p>Model selection has an important impact on subsequent inference. \nIgnoring the model selection step leads to invalid inference. We \ndiscuss some intricate aspects of data-driven model selection that do \nnot seem to have been widely appreciated in the literature. We debunk \nsome myths about model selection, in particular the myth that \nconsistent model selection has no effect on subsequent inference \nasymptotically. We also discuss an \u201cimpossibility\u201d result \nregarding the estimation of the finite-sample distribution of \npost-model-selection estimators.<\/jats:p>","DOI":"10.1017\/s0266466605050036","type":"journal-article","created":{"date-parts":[[2005,4,25]],"date-time":"2005-04-25T10:15:35Z","timestamp":1114424135000},"page":"21-59","source":"Crossref","is-referenced-by-count":524,"title":["MODEL SELECTION AND INFERENCE: FACTS AND FICTION"],"prefix":"10.1017","volume":"21","author":[{"given":"Hannes","family":"Leeb","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benedikt M.","family":"P\u00f6tscher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2005,2,8]]},"reference":[{"key":"S0266466605050036_ref046","doi-asserted-by":"crossref","unstructured":"L\u00fctkepohl, H. 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Manuscript,Department of Statistics, Yale University."},{"key":"S0266466605050036_ref045","unstructured":"Lehmann, E.L. & G. Casella (1998)Theory of Point Estimation.Springer Texts in Statistics.Springer-Verlag."},{"key":"S0266466605050036_ref007","unstructured":"Bunea, F. , X. Niu , & M.H. Wegkamp (2003)The Consistency of the FDR Estimator.Working paper,Department of Statistics, Florida State University at Tallahassee."},{"key":"S0266466605050036_ref054","doi-asserted-by":"crossref","unstructured":"P\u00f6tscher, B.M. (1995)Comment on \u201cThe effect of model selection on confidenceregions and prediction regions.\u201d Econometric Theory 11,550\u2013559.","DOI":"10.1017\/S0266466600009415"},{"key":"S0266466605050036_ref004","doi-asserted-by":"crossref","unstructured":"Andrews, D.W.K. (1986)Complete consistency: A testing analogue of estimator consistency.Review of Economic Studies 53,263\u2013269.","DOI":"10.2307\/2297650"},{"key":"S0266466605050036_ref014","doi-asserted-by":"crossref","unstructured":"Ensor, K.B. & H.J. Newton (1988)The effect of order estimation on estimating the peak frequency ofan autoregressive spectral density.Biometrika 75,587\u2013589.","DOI":"10.2307\/2336611"},{"key":"S0266466605050036_ref003","doi-asserted-by":"crossref","unstructured":"Altissimo, F. & V. Corradi (2003)Strong rules for detecting the numbers of breaks in a time series.Journal of Econometrics 117,207\u2013244.","DOI":"10.1016\/S0304-4076(03)00147-7"},{"key":"S0266466605050036_ref006","doi-asserted-by":"crossref","unstructured":"Bunea, F. (2004)Consistent covariate selection and post model selection inferencein semiparametric regression.Annals of Statistics 32,898\u2013927.","DOI":"10.1214\/009053604000000247"},{"key":"S0266466605050036_ref043","unstructured":"Leeb, H. & B.M. P\u00f6tscher (2003b)Can One Estimate the Conditional Distribution ofPost-Model-Selection Estimators? Working paper,Department of Statistics, University of Vienna. (Also available asCowles Foundation Discussion paper 1444.)"},{"key":"S0266466605050036_ref011","doi-asserted-by":"crossref","unstructured":"Dijkstra, T.K. & J.H. Veldkamp (1988)Data-driven selection of regressors and the bootstrap.Lecture Notes in Economics and Mathematical Systems 307,17\u201338.","DOI":"10.1007\/978-3-642-61564-1_2"},{"key":"S0266466605050036_ref027","unstructured":"Judge, G.G. & T.A. Yancey (1986)Improved Methods of Inference in Econometrics.North-Holland."},{"key":"S0266466605050036_ref063","doi-asserted-by":"crossref","unstructured":"S\u00f6derstr\u00f6m, T. 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(1998)Valid confidence intervals in regression after variable selection.Econometric Theory 14,463\u2013482.","DOI":"10.1017\/S0266466698144031"},{"key":"S0266466605050036_ref025","unstructured":"Hosoya, Y. (1984)Information criteria and tests for time series models. In O.D. Anderson (ed.),Time Series Analysis: Theory and Practice,vol. 5, pp.39\u201352.North-Holland."},{"key":"S0266466605050036_ref031","unstructured":"Kabaila, P. & H. Leeb (2004)On the Large-Sample Minimal Coverage Probability of ConfidenceIntervals after Model Selection.Working paper,Department of Statistics, Yale University."},{"key":"S0266466605050036_ref053","doi-asserted-by":"crossref","unstructured":"P\u00f6tscher, B.M. (1991)Effects of model selection on inference.Econometric Theory 7,163\u2013185.","DOI":"10.1017\/S0266466600004382"},{"key":"S0266466605050036_ref042","doi-asserted-by":"crossref","unstructured":"Leeb, H. & B.M. P\u00f6tscher (2003a)The finite-sample distribution of post-model-selection estimatorsand uniform versus nonuniform approximations.Econometric Theory 19,100\u2013142.","DOI":"10.1017\/S0266466603191050"},{"key":"S0266466605050036_ref023","doi-asserted-by":"crossref","unstructured":"Hidalgo, J. (2002)Consistent order selection with strongly dependent data and itsapplication to efficient estimation.Journal of Econometrics 110,213\u2013239.","DOI":"10.1016\/S0304-4076(02)00094-5"},{"key":"S0266466605050036_ref057","doi-asserted-by":"crossref","unstructured":"Rao, C.R. & Y. Wu (2001)On model selection.IMS Lecture Notes Monograph Series 38,1\u201357.","DOI":"10.1214\/lnms\/1215540960"},{"key":"S0266466605050036_ref038","doi-asserted-by":"crossref","unstructured":"Kulperger, R.J. & S.E. Ahmed (1992)A bootstrap theorem for a preliminary test estimator.Communications in Statistics: Theory and Methods 21,2071\u20132082.","DOI":"10.1080\/03610929208830898"},{"key":"S0266466605050036_ref017","doi-asserted-by":"crossref","unstructured":"Giles, J.A. & D.E.A. Giles (1993)Pre-test estimation and testing in econometrics: Recentdevelopments.Journal of Economic Surveys 7,145\u2013197.","DOI":"10.1111\/j.1467-6419.1993.tb00163.x"},{"key":"S0266466605050036_ref009","doi-asserted-by":"crossref","unstructured":"Corradi, V. (1999)Deciding between I(0) and I(1) via FLIL-basedbounds.Econometric Theory 15,643\u2013663.","DOI":"10.1017\/S0266466699155014"},{"key":"S0266466605050036_ref016","doi-asserted-by":"crossref","unstructured":"Frank, I.E. & J.H. Friedman (1993)A statistical view of some chemometrics regression tools (withdiscussion).Technometrics 35,109\u2013148.","DOI":"10.2307\/1269656"},{"key":"S0266466605050036_ref018","unstructured":"Hajek, J. 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Novak (1998)The distribution of estimators after model selection: Large andsmall sample results.Journal of Statistical Computation and Simulation 60,19\u201356.","DOI":"10.1080\/00949659808811870"},{"key":"S0266466605050036_ref041","unstructured":"Leeb, H. & B.M. P\u00f6tscher (2002)Performance Limits for Estimators of the Risk or Distribution ofShrinkage-Type Estimators, and Some General Lower Risk-BoundResults.Working paper,Department of Statistics, University of Vienna."},{"key":"S0266466605050036_ref015","doi-asserted-by":"crossref","unstructured":"Fan, J. & R. Li (2001)Variable selection via nonconcave penalized likelihood and itsoracle properties.Journal of the American Statistical Association 96,1348\u20131360.","DOI":"10.1198\/016214501753382273"},{"key":"S0266466605050036_ref010","doi-asserted-by":"crossref","unstructured":"Danilov, D. & J.R. Magnus (2004)On the harm that ignoring pretesting can cause.Journal of Econometrics 122,27\u201346.","DOI":"10.1016\/j.jeconom.2003.10.018"},{"key":"S0266466605050036_ref001","doi-asserted-by":"crossref","unstructured":"Ahmed, S.E. & A.K. Basu (2000)Least squares, preliminary test and Stein-type estimation ingeneral vector AR(p) models.Statistica Neerlandica 54,47\u201366.","DOI":"10.1111\/1467-9574.00125"},{"key":"S0266466605050036_ref065","unstructured":"Yang, Y. (2003)Can the Strengths of AIC and BIC Be Shared? Working paper,Department of Statistics, Iowa State University."},{"key":"S0266466605050036_ref039","unstructured":"Leeb, H. 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(1999)The traditional pretest estimator.Teoriya Veroyatnost. i Primenen.44, 401\u2013418;translation in Theory of Probability and ItsApplications 44 (2000), 293\u2013308.","DOI":"10.4213\/tvp775"},{"key":"S0266466605050036_ref002","doi-asserted-by":"crossref","unstructured":"Altissimo, F. & V. Corradi (2002)Bounds for inference with nuisance parameters present only underthe alternative.Econometrics Journal 5,494\u2013519.","DOI":"10.1111\/1368-423X.00095"},{"key":"S0266466605050036_ref024","doi-asserted-by":"crossref","unstructured":"Hjort, N.L. & G. Claeskens (2003)Frequentist model average estimators.Journal of the American Statistical Association 98,879\u2013899.","DOI":"10.1198\/016214503000000828"},{"key":"S0266466605050036_ref040","unstructured":"Leeb, H. 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(2001)Incorporating lag order selection uncertainty in parameterinference for AR models.Economics Letters 72,137\u2013144.","DOI":"10.1016\/S0165-1765(01)00433-5"},{"key":"S0266466605050036_ref060","doi-asserted-by":"crossref","unstructured":"Sen, P.K (1979)Asymptotic properties of maximum likelihood estimators based onconditional specification.Annals of Statistics 7,1019\u20131033.","DOI":"10.1214\/aos\/1176344785"},{"key":"S0266466605050036_ref029","unstructured":"Kabaila, P. (1996)The evaluation of model selection criteria: Pointwise limits inthe parameter space. In D.L. Dowe , K.B. Korb , & J.J. Oliver (eds.),Information, Statistics and Induction in Science, pp.114\u2013118.World Scientific."},{"key":"S0266466605050036_ref005","doi-asserted-by":"crossref","unstructured":"Bauer, P. , B.M. P\u00f6tscher , & P. Hackl (1988)Model selection by multiple test procedures.Statistics 19,39\u201344.","DOI":"10.1080\/02331888808802068"},{"key":"S0266466605050036_ref061","doi-asserted-by":"crossref","unstructured":"Sen, P.K & A.K.M.E. Saleh (1987)On preliminary test and shrinkage M-estimation in linearmodels.Annals of Statistics 15,1580\u20131592.","DOI":"10.1214\/aos\/1176350611"},{"key":"S0266466605050036_ref035","unstructured":"Knight, K. (1999)Epi-convergence in Distribution and Stochastic Equi-semicontinuity.Working paper,Department of Statistics, University of Toronto."},{"key":"S0266466605050036_ref051","unstructured":"P\u00f6tscher, B.M. (1981)Order Estimation in ARMA-Models by Lagrangian Multiplier Tests.Research report 5,Department of Econometrics and Operations Research, University ofTechnology,Vienna."},{"key":"S0266466605050036_ref008","doi-asserted-by":"crossref","unstructured":"Chen, S.S. , D.L. Donoho , & M.A. Saunders (1998)Atomic decomposition by basis pursuit.SIAM Journal on Scientific Computing 20,33\u201361.","DOI":"10.1137\/S1064827596304010"},{"key":"S0266466605050036_ref026","unstructured":"Judge, G.G. & M.E. Bock (1978)The Statistical Implications of Pre-test and Stein-Rule Estimatorsin Econometrics.North-Holland."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466605050036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T01:15:48Z","timestamp":1750468548000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466605050036\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2]]},"references-count":65,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,12]]}},"alternative-id":["S0266466605050036"],"URL":"https:\/\/doi.org\/10.1017\/s0266466605050036","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,2]]}}}