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Highly efficient estimators of multivariate location with high breakdown point. (English) Zbl 0757.62030

Summary: We propose an affine equivariant estimator of multivariate location that combines a high breakdown point and a bounded influence function with high asymptotic efficiency. This proposal is basically a location \(M\)- estimator based on the observations obtained after scaling with an affine equivariant high breakdown covariance estimator. The resulting location estimator will inherit the breakdown point of the initial covariance estimator and within the location-covariance model only the \(M\)-estimator will determine the type of influence function and the asymptotic behaviour. We prove consistency and asymptotic normality and obtain the breakdown point and the influence function.

MSC:

62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
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