IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/9062.html
   My bibliography  Save this paper

Confidence sets based on penalized maximum likelihood estimators

Author

Listed:
  • Pötscher, Benedikt M.
  • Schneider, Ulrike

Abstract

The finite-sample coverage properties of confidence intervals based on penalized maximum likelihood estimators like the LASSO, adaptive LASSO, and hard-thresholding are analyzed. It is shown that symmetric intervals are the shortest. The length of the shortest intervals based on the hard-thresholding estimator is larger than the length of the shortest interval based on the adaptive LASSO, which is larger than the length of the shortest interval based on the LASSO, which in turn is larger than the standard interval based on the maximum likelihood estimator. In the case where the penalized estimators are tuned to possess the `sparsity property', the intervals based on these estimators are larger than the standard interval by an order of magnitude. A simple asymptotic confidence interval construction in the `sparse' case, that also applies to the smoothly clipped absolute deviation estimator, is also discussed.

Suggested Citation

  • Pötscher, Benedikt M. & Schneider, Ulrike, 2008. "Confidence sets based on penalized maximum likelihood estimators," MPRA Paper 9062, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9062
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/9062/1/MPRA_paper_9062.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/16013/2/MPRA_paper_16013.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
    3. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    4. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.
    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. Matei Demetrescu & Uwe Hassler & Vladimir Kuzin, 2011. "Pitfalls of post-model-selection testing: experimental quantification," Empirical Economics, Springer, vol. 40(2), pages 359-372, April.
    2. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    3. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    4. Leeb, Hannes & Pötscher, Benedikt M. & Ewald, Karl, 2014. "On various confidence intervals post-model-selection," MPRA Paper 52858, University Library of Munich, Germany.
    5. Ulrike Schneider, 2016. "Confidence Sets Based on Thresholding Estimators in High-Dimensional Gaussian Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1412-1455, December.
    6. Pötscher, Benedikt M. & Schneider, Ulrike, 2011. "Distributional results for thresholding estimators in high-dimensional Gaussian regression models," MPRA Paper 31882, University Library of Munich, Germany.

    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. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    2. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    3. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    4. Schneider Ulrike & Wagner Martin, 2012. "Catching Growth Determinants with the Adaptive Lasso," German Economic Review, De Gruyter, vol. 13(1), pages 71-85, February.
    5. Kwon, Sunghoon & Lee, Sangin & Kim, Yongdai, 2015. "Moderately clipped LASSO," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 53-67.
    6. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    7. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
    8. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.
    9. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    10. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    11. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2020. "Machine Learning Advances for Time Series Forecasting," Papers 2012.12802, arXiv.org, revised Apr 2021.
    12. Malene Kallestrup-Lamb & Anders Bredahl Kock & Johannes Tang Kristensen, 2016. "Lassoing the Determinants of Retirement," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1522-1561, December.
    13. Audrino, Francesco & Camponovo, Lorenzo & Roth, Constantin, 2015. "Testing the lag structure of assets’ realized volatility dynamics," Economics Working Paper Series 1501, University of St. Gallen, School of Economics and Political Science.
    14. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," DSSR Discussion Papers 96, Graduate School of Economics and Management, Tohoku University.
    15. Ulrike Schneider, 2016. "Confidence Sets Based on Thresholding Estimators in High-Dimensional Gaussian Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1412-1455, December.
    16. Kun Chen & Kung-Sik Chan & Nils Chr. Stenseth, 2014. "Source-Sink Reconstruction Through Regularized Multicomponent Regression Analysis-With Application to Assessing Whether North Sea Cod Larvae Contributed to Local Fjord Cod in Skagerrak," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 560-573, June.
    17. Chatterjee, A. & Gupta, S. & Lahiri, S.N., 2015. "On the residual empirical process based on the ALASSO in high dimensions and its functional oracle property," Journal of Econometrics, Elsevier, vol. 186(2), pages 317-324.
    18. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(3), pages 1-16, June.
    19. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    20. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," ISER Discussion Paper 1053r, Institute of Social and Economic Research, Osaka University, revised Mar 2020.

    More about this item

    Keywords

    penalized maximum likelihood; Lasso; adaptive Lasso; hard-thresholding; confidence set; coverage probability; sparsity; model selection;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:9062. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.