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Fast algorithms for the minimum volume estimator

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  • Selin Ahipaşaoğlu

Abstract

The minimum volume ellipsoid (MVE) estimator is an important tool in robust regression and outlier detection in statistics. We develop fast and efficient algorithms for the MVE estimator problem and discuss how they can be implemented efficiently. The novelty of our approach stems from the recent developments in the first-order algorithms for solving the related minimum volume enclosing ellipsoid problem. Comparative computational results are provided which demonstrate the strength of the algorithms. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:2:p:351-370
    DOI: 10.1007/s10898-014-0233-8
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    References listed on IDEAS

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    1. Eligius M.T. Hendrix & Boglárka G.-Tóth, 2010. "Introduction to Nonlinear and Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-88670-1, June.
    2. Leonid G. Khachiyan, 1996. "Rounding of Polytopes in the Real Number Model of Computation," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 307-320, May.
    3. Cook, R. D. & Hawkins, D. M. & Weisberg, S., 1993. "Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 213-218, February.
    4. Torti, Francesca & Perrotta, Domenico & Atkinson, Anthony C. & Riani, Marco, 2012. "Benchmark testing of algorithms for very robust regression: FS, LMS and LTS," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2501-2512.
    5. Harman, Radoslav & Pronzato, Luc, 2007. "Improvements on removing nonoptimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 90-94, January.
    6. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.
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