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Matrix strategies for computing the least trimmed squares estimation of the general linear and SUR models

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  • Hofmann, Marc
  • Kontoghiorghes, Erricos John

Abstract

An algorithm for computing the exact least trimmed squares (LTS) estimator of the standard regression model has recently been proposed. The LTS algorithm is adapted to the general linear and seemingly unrelated regressions models with possible singular dispersion matrices. It searches through a regression tree to find the optimal estimates and has combinatorial complexity. The model is formulated as a generalized linear least squares problem. Efficient matrix techniques are employed to update the generalized residual sum of squares of a subset model. Specifically, the new algorithm utilizes previous computations to update a generalized QR decomposition by a single row. The sparse structure of the model is exploited. Theoretical measures of computational complexity are provided. Experimental results confirm the ability of the new algorithms to identify outlying observations.

Suggested Citation

  • Hofmann, Marc & Kontoghiorghes, Erricos John, 2010. "Matrix strategies for computing the least trimmed squares estimation of the general linear and SUR models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3392-3403, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3392-3403
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    References listed on IDEAS

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    1. Cristian Gatu & Erricos Kontoghiorghes, 2002. "A branch and bound algorithm for computing the best subset regression models," Computing in Economics and Finance 2002 294, Society for Computational Economics.
    2. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    3. Kontoghiorghes, E. J. & Clarke, M. R. B., 1995. "An alternative approach for the numerical solution of seemingly unrelated regression equations models," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 369-377, April.
    4. Foschi, Paolo & Kontoghiorghes, Erricos J., 2002. "Seemingly unrelated regression model with unequal size observations: computational aspects," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 211-229, November.
    5. Foschi, Paolo & Belsley, David A. & Kontoghiorghes, Erricos J., 2003. "A comparative study of algorithms for solving seemingly unrelated regressions models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 3-35, October.
    6. Srivastava, V. K. & Dwivedi, T. D., 1979. "Estimation of seemingly unrelated regression equations : A brief survey," Journal of Econometrics, Elsevier, vol. 10(1), pages 15-32, April.
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    Cited by:

    1. Klouda, Karel, 2015. "An exact polynomial time algorithm for computing the least trimmed squares estimate," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 27-40.
    2. Mount, David M. & Netanyahu, Nathan S. & Piatko, Christine D. & Wu, Angela Y. & Silverman, Ruth, 2016. "A practical approximation algorithm for the LTS estimator," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 148-170.

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