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arXiv · 1203.4160

A Novel Robust Approach to Least Squares Problems with Bounded Data Uncertainties

Nargiz Kalantarova·Mehmet A. Donmez·Suleyman S. Kozat
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Abstract

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes a worst case difference regret. The regret is defined as the difference between a squared data error and the smallest attainable squared data error of a least squares estimator. We then propose a robust regularized least squares approach to the regularized least squares problem under data uncertainties by using a similar framework. We show that both unstructured and structured robust least squares problems and robust regularized least squares problem can be put in certain semi-definite programming forms. Through several simulations, we demonstrate the merits of the proposed algorithms with respect to the the well-known alternatives in the literature.

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Nargiz Kalantarova, Mehmet A. Donmez, Suleyman S. Kozat. 2012-03-19. A Novel Robust Approach to Least Squares Problems with Bounded Data Uncertainties. https://arxiv.org/abs/1203.4160

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