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The influence functions for the least trimmed squares and the least trimmed absolute deviations estimators. (English) Zbl 0803.62027

Summary: The influence functions for Rousseeuw’s least trimmed squares estimator [P. J. Rousseeuw and A. M. Leroy, Robust regression and outlier detection. (1987; Zbl 0711.62030)] and for the author’s [Stat. Probab. Lett. 19, No. 5, 387-398 (1994; Zbl 0797.62029)] least trimmed absolute deviations 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 F. R. Hampel et al. [Robust statistics. The approach based on influence functions. (1986; Zbl 0593.62027)]. 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.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
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