THE INFLUENCE FUNCTIONS FOR THE LEAST TRIMMED SQUARES AND THE LEAST TRIMMED ABSOLUTE DEVIATIONS ESTIMATORS

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 et al. (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.