Pivotal estimation in high-dimensional regression via linear programming
AbstractWe propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is faster than for previously known techniques using conic programs, and it allows one to deal with higher dimensional models. We provide upper bounds for estimation and prediction errors of the proposed estimator showing that it achieves the same rate as in the more restrictive situation of fixed design and i.i.d. Gaussian errors with known variance. Following Gautier and Tsybakov (2011), we obtain the results under weaker sensitivity assumptions than the restricted eigenvalue or assimilated conditions.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1303.7092.
Date of creation: Mar 2013
Date of revision: Apr 2013
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Web page: http://arxiv.org/
Other versions of this item:
- Eric Gautier & Alexandre Tsybakov, 2013. "Pivotal estimation in high-dimensional regression via linear programming," Working Papers hal-00805556, HAL.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Eric Gautier & Alexandre Tsybakov, 2011.
"High-Dimensional Instrumental Variables Regression and Confidence Sets,"
2011-13, Centre de Recherche en Economie et Statistique.
- Eric Gautier & Alexandre Tsybakov, 2011. "High-dimensional instrumental variables regression and confidence sets," Working Papers hal-00591732, HAL.
- A. Belloni & D. Chen & Victor Chernozhukov & Christian Hansen, 2010.
"Sparse models and methods for optimal instruments with an application to eminent domain,"
CeMMAP working papers
CWP31/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
- A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
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