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Confidence sets based on penalized maximum likelihood estimators

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/16013/2/MPRA_paper_16013.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.
    5. 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.
    6. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
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    Citations

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    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.

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    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

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