Davies, Laurie The asymptotics of Rousseeuw’s minimum volume ellipsoid estimator. (English) Zbl 0764.62046 Ann. Stat. 20, No. 4, 1828-1843 (1992). 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. Cited in 41 Documents 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 Keywords:weak convergence; non-Gaussian limiting distribution; minimum volume ellipsoid; affine invariant metrics; cube root convergence; minimum volume estimator; location; dispersion; highest possible breakdown point; affine equivariant estimator; local Hölder condition of order 1/2 Citations:Zbl 0609.62054 PDFBibTeX XMLCite \textit{L. Davies}, Ann. Stat. 20, No. 4, 1828--1843 (1992; Zbl 0764.62046) Full Text: DOI