Abstract
Several iterative procedures have been proposed and developed to solve numerically the problem of robust regression, in particular, of robust linear regression. The algorithms described here are modified versions of the “sophisticated method” given by Huber (1973, [8]) which sometimes fail to converge. In this paper, the new algorithms are formulated and convergence proofs are given. The behavior of the procedures is illustrated by a numerical example and is compared to another (“simple”) algorithm.
Zusammenfassung
Verschiedene iterative Prozeduren zur numerischen Lösung des Problems der robusten Regression, genauer der robusten linearen Regression, wurden vorgeschlagen und entwickelt. Die hier beschriebenen Algorithmen sind modifizierte Fassungen der in der Veröffentlichung von Huber (1973, [8]) beschriebenen raffinierten („sophisticated”) Methode, die aber manchmal nicht konvergiert. In der vorliegenden Arbeit werden neue Algorithmen formuliert und Konvergenzbeweise gegeben. Das Verhalten der Prozeduren wird an einem numerischen Beispiel illustriert und mit dem eines einfachen („simple”) Algorithmus verglichen.
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Work supported by the Swiss National Science Foundation, Contract No. 2.836.73.
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Dutter, R. Algorithms for the Huber estimator in multiple regression. Computing 18, 167–176 (1977). https://doi.org/10.1007/BF02243626
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DOI: https://doi.org/10.1007/BF02243626