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2011 Distributional results for thresholding estimators in high-dimensional Gaussian regression models
Benedikt M. Pötscher, Ulrike Schneider
Electron. J. Statist. 5: 1876-1934 (2011). DOI: 10.1214/11-EJS659

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 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 uniform convergence rate under either type of tuning.

Citation

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Benedikt M. Pötscher. Ulrike Schneider. "Distributional results for thresholding estimators in high-dimensional Gaussian regression models." Electron. J. Statist. 5 1876 - 1934, 2011. https://doi.org/10.1214/11-EJS659

Information

Published: 2011
First available in Project Euclid: 30 December 2011

zbMATH: 1271.62149
MathSciNet: MR2970179
Digital Object Identifier: 10.1214/11-EJS659

Subjects:
Primary: 62F11, 62F12
Secondary: 62E15, 62E20, 62J05, 62J07

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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