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On the distribution of the adaptive LASSO estimator

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Author Info
Pötscher, Benedikt M.
Schneider, Ulrike

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Abstract

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than n^{-1/2} in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the `oracle' property of the adaptive LASSO estimator established in Zou 2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6913.

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Date of creation: Dec 2007
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Handle: RePEc:pra:mprapa:6913

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Related research
Keywords: Penalized maximum likelihood LASSO adaptive LASSO nonnegative garotte finite-sample distribution asymptotic distribution oracle property estimation of distribution uniform consistency.

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Find related papers by JEL classification:
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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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. 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. [Downloadable!]
  2. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July. [Downloadable!] (restricted)
  3. 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)
  4. 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)
  5. 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)
  6. 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!]
  7. Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Oxford University Press for Biometrika Trust, vol. 94(1), pages 19-35. [Downloadable!] (restricted)
  8. Hannes Leeb & Benedikt M. Potscher, 2003. "Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?," Cowles Foundation Discussion Papers 1444, Cowles Foundation, Yale University. [Downloadable!]
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  9. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany. [Downloadable!]
  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. 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., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(01), pages 100-142, January. [Downloadable!]
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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, 2008. "Confidence sets based on penalized maximum likelihood estimators," MPRA Paper 9062, University Library of Munich, Germany. [Downloadable!]
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