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Confidence Sets Based on Sparse Estimators Are Necessarily Large

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Author Info
Pötscher, Benedikt M.

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Abstract

Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are set in a general parametric or semiparametric framework.

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File URL: http://mpra.ub.uni-muenchen.de/5677/
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File URL: http://mpra.ub.uni-muenchen.de/15087/
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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5677.

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Date of creation: Aug 2007
Date of revision: Apr 2009
Handle: RePEc:pra:mprapa:5677

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Related research
Keywords: sparse estimator; consistent model selection; post-model-selection estimator; penalized maximum likelihood; confidence set; coverage probability;

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Find related papers by JEL classification:
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. repec:cup:etheor:v:11:y:1995:i:3:p:537-49 is not listed on IDEAS
  3. Kabaila, Paul & Leeb, Hannes, 2006. "On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 619-629, June. [Downloadable!] (restricted)
  4. Kabaila, Paul, 1995. "The Effect of Model Selection on Confidence Regions and Prediction Regions," Econometric Theory, Cambridge University Press, vol. 11(03), pages 537-549, June. [Downloadable!]
  5. Bunea, Florentina & McKeague, Ian W., 2005. "Covariate selection for semiparametric hazard function regression models," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 186-204, January. [Downloadable!] (restricted)
  6. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January. [Downloadable!] (restricted)
  7. P?tscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June. [Downloadable!]
  8. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September. [Downloadable!] (restricted)
  9. Hansheng Wang & Guodong Li & Chih-Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78. [Downloadable!] (restricted)
  10. Hannes Leeb & Benedikt M. Poetscher, 2005. "Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator," Cowles Foundation Discussion Papers 1500, Cowles Foundation, Yale University, revised Apr 2007. [Downloadable!]
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  11. 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. [Downloadable!] (restricted)
  12. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Oxford University Press for Biometrika Trust, vol. 94(3), pages 553-568. [Downloadable!] (restricted)
  13. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February. [Downloadable!]
  14. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(04), pages 463-482, August. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany, revised Dec 2008. [Downloadable!]
  2. Pötscher, Benedikt M. & Schneider, Ulrike, 2008. "Confidence sets based on penalized maximum likelihood estimators," MPRA Paper 9062, University Library of Munich, Germany, revised May 2009. [Downloadable!]
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