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On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding

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Author Info
Pötscher, Benedikt M.
Leeb, Hannes

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Abstract

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conservative model selection. Our findings complement those of Knight and Fu (2000) and Fan and Li (2001). We show that the distributions are typically highly nonnormal regardless of how the estimator is tuned, and that this property persists in large samples. An impossibility result regarding estimation of the estimators' distribution function is also provided.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5615.

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Date of creation: Oct 2007
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Handle: RePEc:pra:mprapa:5615

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Related research
Keywords: Penalized maximum likelihood LASSO SCAD thresholding post-model-selection estimator finite-sample distribution asymptotic distribution estimation of distribution uniform consistency

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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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. 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!]
  3. 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!]
  4. repec:cup:etheor:v:11:y:1995:i:3:p:537-49 is not listed on IDEAS
  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. [Downloadable!] (restricted)
  6. 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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