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      Robust least squares methods under bounded data uncertainties

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      Author
      Vanli, N. D.
      Donmez, M. A.
      Kozat, S. S.
      Date
      2015
      Source Title
      Digital Signal Processing
      Print ISSN
      1051-2004
      Publisher
      Academic Press
      Volume
      36
      Pages
      82 - 92
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations.
      Keywords
      Data estimation
      Least squares
      Additive noise
      Estimation
      Matrix algebra
      Optimization
      Minimax
      Regret
      Robust
      Least squares approximations
      Permalink
      http://hdl.handle.net/11693/23580
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.dsp.2014.10.004
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      • Department of Electrical and Electronics Engineering 3524
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