IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0611186.html
   My bibliography  Save this paper

The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations

Author

Listed:
  • Hannes Leeb

Abstract

We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We then analyze the large-sample limit behavior of these cdfs, in the fixed-parameter case and under local alternatives.

Suggested Citation

  • Hannes Leeb, 2006. "The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations," Papers math/0611186, arXiv.org.
    • Handle: RePEc:arx:papers:math/0611186
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0611186
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    2. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    3. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    4. Leeb, Hannes & Pötscher, Benedikt M. & Ewald, Karl, 2014. "On various confidence intervals post-model-selection," MPRA Paper 58326, University Library of Munich, Germany, revised 2014.
    5. Patrik Guggenberger, "undated". "Hybrid and size-corrected subsample methods (joint with D.W.K. Andrews), June 2005, this version March 2007," UCLA Economics Online Papers 400, UCLA Department of Economics.
    6. Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.
    7. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation for Research in Economics, Yale University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    2. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2019. "Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 749-758, April.
    3. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    4. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
    5. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    6. Chenchuan (Mark) Li & Ulrich K. Müller, 2021. "Linear regression with many controls of limited explanatory power," Quantitative Economics, Econometric Society, vol. 12(2), pages 405-442, May.
    7. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    8. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    9. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    10. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    11. Jan R. Magnus, 2019. "On Using the t -Ratio as a Diagnostic," Econometrics, MDPI, vol. 7(2), pages 1-3, May.
    12. Alain Guay, 2020. "Identification of Structural Vector Autoregressions Through Higher Unconditional Moments," Working Papers 20-19, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    13. Susanne M. Schennach & Daniel Wilhelm, 2017. "A Simple Parametric Model Selection Test," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1663-1674, October.
    14. Michael C. Knaus, 2021. "A double machine learning approach to estimate the effects of musical practice on student’s skills," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 282-300, January.
    15. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    16. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    17. Michael C Knaus & Michael Lechner & Anthony Strittmatter, 2021. "Machine learning estimation of heterogeneous causal effects: Empirical Monte Carlo evidence," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 134-161.
    18. Doppelhofer, G. & Weeks, M., 2005. "Jointness of Growth Determinants," Cambridge Working Papers in Economics 0542, Faculty of Economics, University of Cambridge.
    19. Toshiaki Tsukurimichi & Yu Inatsu & Vo Nguyen Le Duy & Ichiro Takeuchi, 2022. "Conditional selective inference for robust regression and outlier detection using piecewise-linear homotopy continuation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1197-1228, December.
    20. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:math/0611186. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.