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Original Articles

Global non-smooth optimization in robust multivariate regression

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Pages 124-138 | Received 10 Sep 2010, Accepted 11 Aug 2011, Published online: 10 Oct 2011

References

  • Agulló , J. 2001 . New algorithms for computing the least trimmed squares regression estimator . Comput. Statist. Data Anal , 36 : 425 – 439 .
  • Agulló , J. , Croux , C. and Van Aelst , S. 2008 . The multivariate least-trimmed squares estimator . J. Multivariate Anal , 99 : 311 – 338 .
  • Bagirov , A. 2002 . A method for minimization of quasi-differentiable functions . Optim. Methods Softw , 17 : 31 – 60 .
  • Bagirov , A. and Rubinov , A. 2000 . Global minimization of increasing positively homogeneous function over the unit simplex . Ann. Oper. Res , 98 : 171 – 187 .
  • Bagirov , A. and Rubinov , A. 2003 . Cutting angle method and a local search . J. Global Optim , 27 : 193 – 213 .
  • Beliakov , G. 2004 . The cutting angle method – a tool for constrained global optimization . Optim. Methods Softw , 19 : 137 – 151 .
  • Beliakov , G. 2005 . “ A review of applications of the cutting angle methods ” . In Continuous Optimization , 209 – 248 . New York : Springer .
  • Beliakov , G. 2008 . Extended cutting angle method of global optimization . Pacific J. Optim , 4 : 153 – 176 .
  • Beliakov , G. and Ugon , J. 2007 . Implementation of novel methods of global and non-smooth optimization: GANSO programming library . Optimization , 56 : 543 – 546 .
  • Bernholt , T. 2005 . “ Robust estimators are hard to compute ” . In Tech. Rep , University of Dortmund . Available at http://ls2-www.cs.tu-dortmund.de/ bernholt/ps/tr52-05.pdf
  • Cerioli , A. 2010 . Multivariate outlier detection with high-breakdown estimators . J. Amer. Statist. Assoc , 105 : 147 – 156 .
  • Conn , A. , Scheinberg , K. and Vicente , L. 2009 . Introduction to derivative-free optimization , Philadelphia , PA : SIAM .
  • Gervini , D. and Yohai , V. 2002 . A class of robust and fully efficient regression estimators . Ann. Statist , 30 : 583 – 616 .
  • Hadi , A. and Luceño , A. 1997 . Maximum trimmed likelihood estimators: A unified approach, examples, and algorithms . Comput. Statist. Data Anal , 25 : 251 – 272 .
  • Hampel , F. 1971 . A general qualitative definition of robustness . Ann. Math. Statist , 42 : 1887 – 1896 .
  • Hawkins , D. M. and Olive , D. J. 1999 . Applications and algorithms for least trimmed sum of absolute deviations regression . Comput. Statist. Data Anal , 32 : 119 – 134 .
  • Hofmann , M. , Gatu , C. and Kontoghiorghes , E. 2010 . An exact least trimmed squares algorithm for a range of coverage values . J. Comput. Graph. Statist , 19 : 191 – 204 .
  • Kiwiel , K. 1985 . Methods of descent for non-differentiable optimization , Berlin : Springer-Verlag .
  • Makela , M. and Neittaanmaki , P. 1992 . Nonsmooth optimization: analysis and algorithms with applications to optimal control , River Edge , NJ : World Scientific .
  • Mammadov , M. , Rubinov , A. and Yearwood , J. 2005 . “ Dynamical systems described by relational elasticities with applications to global optimization ” . In Continuous Optimisation: Current Trends and Modern Applications , 365 – 385 . New York : Springer .
  • Maronna , R. , Martin , R. and Yohai , V. 2006 . Robust statistics: theory and methods , New York : Wiley .
  • Moré , J. and Wild , S. 2009 . Benchmarking derivative-free optimization algorithms . SIAM J. Optim , 20 : 172 – 191 .
  • Nelder , J. A. and Mead , R. 1965 . A simplex method for function minimization . Comput. J , 7 : 308 – 313 .
  • Nguyen , T. D. and Welsch , R. 2010 . Outlier detection and least trimmed squares approximation using semi-definite programming . Comput. Statist. Data Anal , 12 : 3212 – 3226 .
  • Nunkesser , R. and Morell , O. 2010 . An evolutionary algorithm for robust regression . Comput. Statist. Data Anal , 54 : 3242 – 3248 .
  • Pijavski , S. 1972 . An algorithm for finding the absolute extremum of a function . USSR Comput. Math. Math. Phys , 2 : 57 – 67 .
  • Powell , M. 2006 . “ The NEWUOA software for unconstrained optimization without derivatives ” . In Large-Scale Nonlinear Optimization , 255 – 297 . USA : Springer .
  • Press , A. , Teukolsky , S. , Vetterling , W. and Flannery , B. 2002 . Numerical recipes in C: the art of scientific computing , New York : Cambridge University Press .
  • Rousseeuw , P. 1984 . Least median of squares regression . J. Amer. Statist. Assoc , 79 : 871 – 880 .
  • Rousseeuw , P. and Leroy , A. 2003 . Robust regression and outlier detection , New York : Wiley .
  • Rousseeuw , P. and Van Driessen , K. 2006 . Computing LTS regression for large data sets . Data Min. Knowl. Discov , 12 : 29 – 45 .
  • Rubinov , A. 2000 . Abstract convexity and global optimization , Dordrecht : Kluwer .
  • Salibian-Barrera , M. and Yohai , V. 2006 . A fast algorithm for S-regression estimates . J. Comput. Graph. Statist , 15 : 414 – 427 .
  • Salibian-Barrera , M. , Willems , G. and Zamar , R. 2008 . The Fast-t estimator for regression . J. Comput. Graph. Statist , 17 : 659 – 682 .
  • Schyns , M. , Haesbroeck , G. and Critchley , F. 2010 . RelaxMCD: Smooth optimisation for the minimum covariance determinant estimator . Comput. Statist. Data Anal , 54 : 843 – 857 .
  • Shubert , B. 1972 . A sequential method seeking the global maximum of a function . SIAM J. Numer. Anal , 9 : 379 – 388 .
  • Stromberg , A. , Hossjer , O. and Hawkins , D. M. 2000 . The least trimmed differences regression estimator and alternatives . J. Amer. Statist. Assoc , 95 : 853 – 864 .
  • Yager , R. and Beliakov , G. 2010 . OWA operators in regression problems . IEEE Trans. Fuzzy Syst , 18 : 106 – 113 .
  • Yohai , V. 1987 . High breakdown-point and high efficiency robust estimates for regression . Ann. Statist , 15 : 642 – 656 .
  • Yohai , V. and Zamar , R. 1988 . High breakdown-point estimates of regression by means of the minimization of an efficient scale . J. Amer. Statist. Assoc , 83 : 406 – 413 .

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