Pötscher, Benedikt M. and Schneider, Ulrike (2008): Confidence sets based on penalized maximum likelihood estimators.
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Abstract
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hardthresholding are analyzed. In the knownvariance case, the finitesample coverage properties of such intervals are determined and it is shown that symmetric intervals are the shortest. The length of the shortest intervals based on the hardthresholding 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. Furthermore, a simple asymptotic confidence interval construction in the `sparse' case, that also applies to the smoothly clipped absolute deviation estimator, is discussed. The results for the knownvariance case are shown to carry over to the unknownvariance case in an appropriate asymptotic sense.
Item Type:  MPRA Paper 

Original Title:  Confidence sets based on penalized maximum likelihood estimators 
Language:  English 
Keywords:  penalized maximum likelihood, Lasso, adaptive Lasso, hardthresholding, confidence set, coverage probability, sparsity, model selection. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  16013 
Depositing User:  Benedikt Poetscher 
Date Deposited:  05. Jul 2009 18:44 
Last Modified:  20. Feb 2013 18:20 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/16013 
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Confidence sets based on penalized maximum likelihood estimators. (deposited 11. Jun 2008 07:29)
 Confidence sets based on penalized maximum likelihood estimators. (deposited 05. Jul 2009 18:44) [Currently Displayed]