Pivotal estimation in high-dimensional regression via linear programming

Eric Gautier and Alexandre Tsybakov

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Abstract: We 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.

Keywords: Heteroscedasticity; High-dimensional models; Linear models; Model selection; Non-Gaussian errors; Pivotal estimation (search for similar items in EconPapers)
Date: 2013-03-26
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-00805556v2
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Citations: View citations in EconPapers (7)

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Working Paper: Pivotal estimation in high-dimensional regression via linear programming (2013)
Working Paper: Pivotal Estimation in High-Dimensional Regression via Linear Programming (2013)
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