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The asymptotics of Rousseeuw’s minimum volume ellipsoid estimator. (English) Zbl 0764.62046

Summary: P. Rousseeuw’s [Mathematical statistics and applications, Proc. 4th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf/Austria 1983, Vol. B, 283- 297 (1985; Zbl 0609.62054)] minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Hölder condition of order 1/2 and converges weakly at the rate of \(n^{-1/3}\) to a non-Gaussian distribution.

MSC:

62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
60F05 Central limit and other weak theorems

Citations:

Zbl 0609.62054
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