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2015 Normalized and standard Dantzig estimators: Two approaches
Jan Mielniczuk, Hubert Szymanowski
Electron. J. Statist. 9(1): 1335-1356 (2015). DOI: 10.1214/15-EJS1040

Abstract

We reconsider the definition of the Dantzig estimator and show that, in contrast to the LASSO, standardization of an experimental matrix leads in general to a different estimator than in the case when it is based on the original data. The properties of the first method, resulting in what is called here the normalized Dantzig estimator are studied and the results on its estimation and prediction error are compared with similar results for the standard version. It is shown that in general the normalized version yields tighter estimation and prediction bounds than the other approach. In the correct specification case tighter bounds are obtained for the normalized Dantzig estimator than for the LASSO. Numerical examples indicate that in the case of imbalanced data the normalized estimator also performs better than the standard version.

Citation

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Jan Mielniczuk. Hubert Szymanowski. "Normalized and standard Dantzig estimators: Two approaches." Electron. J. Statist. 9 (1) 1335 - 1356, 2015. https://doi.org/10.1214/15-EJS1040

Information

Received: 1 October 2013; Published: 2015
First available in Project Euclid: 22 June 2015

zbMATH: 1327.62408
MathSciNet: MR3358327
Digital Object Identifier: 10.1214/15-EJS1040

Subjects:
Primary: 62J05, 62J07
Secondary: 90C25

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 1 • 2015
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