Pötscher, Benedikt M. and Schneider, Ulrike (2011): Distributional results for thresholding estimators in highdimensional Gaussian regression models.
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Abstract
We study the distribution of hard, soft, and adaptive softthresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known errorvariance, we define and study versions of the estimators when the errorvariance is unknown. We derive the finitesample distribution of each estimator and study its behavior in the largesample limit, also investigating the effects of having to estimate the variance when the degrees of freedom nk does not tend to infinity or tends to infinity very slowly. Our analysis encompasses both the case where the estimators are tuned to perform consistent variable selection and the case where the estimators are tuned to perform conservative variable selection. Furthermore, we discuss consistency, uniform consistency and derive the minimax rate under either type of tuning.
Item Type:  MPRA Paper 

Original Title:  Distributional results for thresholding estimators in highdimensional Gaussian regression models 
Language:  English 
Keywords:  Thresholding, Lasso, adaptive Lasso, penalized maximum likelihood, variable selection, finitesample distribution, asymptotic distribution, variance estimation, minimax rate, highdimensional model, oracle property 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C20  General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection 
Item ID:  34600 
Depositing User:  Benedikt Poetscher 
Date Deposited:  08 Nov 2011 20:13 
Last Modified:  22 Oct 2017 06:21 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/34600 
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Distributional results for thresholding estimators in highdimensional Gaussian regression models. (deposited 28 Jun 2011 13:40)
 Distributional results for thresholding estimators in highdimensional Gaussian regression models. (deposited 08 Nov 2011 20:13) [Currently Displayed]