Abstract
Regression techniques with high breakdown point can withstand a substantial amount of outliers in the data. One such method is the least trimmed squares estimator. Unfortunately, its exact computation is quite difficult because the objective function may have a large number of local minima. Therefore, we have been using an approximate algorithm based on p-subsets. In this paper we prove that the algorithm shares the equivariance and good breakdown properties of the exact estimator. The same result is also valid for other high-breakdown-point estimators. Finally, the special case of one-dimensional location is discussed separately because of unexpected results concerning half samples.
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