An efficient Fréchet differentiable high breakdown multivariate location and dispersion estimator

Laurie Davies

Journal of Multivariate Analysis, 1992, vol. 40, issue 2, 311-327

Abstract: A good robust functional should, if possible, be efficient at the model, smooth, and have a high breakdown point. M-estimators can be made efficient and Fréchet differentiable by choosing appropriate [psi]-functions but they have a breakdown point of at most 1/(p + 1) in p dimensions. On the other hand, the local smoothness of known high breakdown functionals has not been investigated. It is known that Rousseeuw's minimum volume ellipsoid estimator is not differentiable and that S-estimators based on smooth functions force a trade-off between efficiency and breakdown point. However, by using a two-step M-estimator based on the minimum volume ellipsoid we show that it is possible to obtain a highly efficient, Fréchet differentiable estimator whilst still retaining the breakdown point. This result is extended to smooth S-estimators.

Keywords: location; parameters; dispersion; parameters; efficiency; Frechet; differentiability; breakdown; point; k-step; M-estimators; S-estimators (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (2)

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