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 the 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. The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
6913.
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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