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The influence functions for the least trimmed squares and the least trimmed absolute deviations estimators

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  • Tableman, Mara

Abstract

The influence functions for Rousseeuw's (1987) least trimmed squares (LTS) estimator and for Tableman's (1994) least trimmed absolute deviations (LTAD) estimator are derived in the univariate case. The half-sample estimators which possess, by construction, the 50% breakdown point property satisfy three of the four robustness criteria defined by Hampel (1986). They have bounded influence functions, finite gross-error sensitivity, and finite rejection point. However, they have infinite local-shift sensitivity. Hence, these estimates can be highly sensitive to small perturbations in the data. Small shifts in centrally located data (inliers) can cause their values to change by relatively large (though bounded) amounts.

Suggested Citation

  • Tableman, Mara, 1994. "The influence functions for the least trimmed squares and the least trimmed absolute deviations estimators," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 329-337, March.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:4:p:329-337
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    Citations

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    Cited by:

    1. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    2. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Discussion Paper 2004-72, Tilburg University, Center for Economic Research.
    3. Wang, Yong & Fu, Chengqun & Guo, Jie & Yu, Qin, 2016. "A robust regression based on weighted LSSVM and penalized trimmed squaresAuthor-Name: Liu, Jianyong," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 328-334.
    4. Olive, David J. & Hawkins, Douglas M., 2003. "Robust regression with high coverage," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 259-266, July.
    5. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    6. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
    7. C. Chatzinakos & L. Pitsoulis & G. Zioutas, 2016. "Optimization techniques for robust multivariate location and scatter estimation," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1443-1460, May.

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