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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© 1991 Springer-Verlag New York, Inc.
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Rousseeuw, P.J., Bassett, G.W. (1991). Robustness of the p-Subset Algorithm for Regression with High Breakdown Point. In: Directions in Robust Statistics and Diagnostics. The IMA Volumes in Mathematics and its Applications, vol 34. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4444-8_10
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DOI: https://doi.org/10.1007/978-1-4612-4444-8_10
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