Robust Estimators are Hard to Compute
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Date
2006-01-25T12:51:23Z
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Abstract
In modern statistics, the robust estimation of parameters of a re-
gression hyperplane is a central problem. Robustness means that the
estimation is not or only slightly a®ected by outliers in the data. In
this paper, it is shown that the following robust estimators are hard
to compute: LMS, LQS, LTS, LTA, MCD, MVE, Constrained M es-
timator, Projection Depth (PD) and Stahel-Donoho. In addition, a
data set is presented such that the ltsReg-procedure of R has proba-
bility less than 0.0001 of ¯nding a correct answer. Furthermore, it is
described, how to design new robust estimators.
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algorithms, complexity theory, computational statistics, robust statistics, search heuristics