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2016 Thresholding least-squares inference in high-dimensional regression models
Mihai Giurcanu
Electron. J. Statist. 10(2): 2124-2156 (2016). DOI: 10.1214/16-EJS1160

Abstract

We propose a thresholding least-squares method of inference for high-dimensional regression models when the number of parameters, $p$, tends to infinity with the sample size, $n$. Extending the asymptotic behavior of the F-test in high dimensions, we establish the oracle property of the thresholding least-squares estimator when $p=o(n)$. We propose two automatic selection procedures for the thresholding parameter using Scheffé and Bonferroni methods. We show that, under additional regularity conditions, the results continue to hold even if $p=\exp(o(n))$. Lastly, we show that, if properly centered, the residual-bootstrap estimator of the distribution of thresholding least-squares estimator is consistent, while a naive bootstrap estimator is inconsistent. In an intensive simulation study, we assess the finite sample properties of the proposed methods for various sample sizes and model parameters. The analysis of a real world data set illustrates an application of the methods in practice.

Citation

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Mihai Giurcanu. "Thresholding least-squares inference in high-dimensional regression models." Electron. J. Statist. 10 (2) 2124 - 2156, 2016. https://doi.org/10.1214/16-EJS1160

Information

Received: 1 January 2016; Published: 2016
First available in Project Euclid: 18 July 2016

zbMATH: 1347.62131
MathSciNet: MR3522671
Digital Object Identifier: 10.1214/16-EJS1160

Subjects:
Primary: 62J05
Secondary: 62E20

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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