Distributional results for thresholding estimators in high-dimensional Gaussian regression models

Benedikt Pötscher and Ulrike Schneider

MPRA Paper from University Library of Munich, Germany

Abstract: We study the distribution of hard-, soft-, and adaptive soft-thresholding 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 error-variance, we define and study versions of the estimators when the error-variance is unknown. We derive the finite-sample distribution of each estimator and study its behavior in the large-sample limit, also investigating the effects of having to estimate the variance when the degrees of freedom n-k 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 model selection and the case where the estimators are tuned to perform conservative model selection. Furthermore, we discuss consistency, uniform consistency and derive the minimax rate under either type of tuning.

Keywords: Thresholding; Lasso; adaptive Lasso; penalized maximum likelihood; finite-sample distribution; asymptotic distribution; variance estimation; minimax rate; high-dimensional model; oracle property (search for similar items in EconPapers)
JEL-codes: C13 C20 C52 (search for similar items in EconPapers)
Date: 2011-06
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (5)

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https://mpra.ub.uni-muenchen.de/34600/2/MPRA_paper_34600.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/34706/1/MPRA_paper_34706.pdf revised version (application/pdf)

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