A practical affine equivariant multivariate median. (English) Zbl 1036.62045

Hettmansperger, Thomas P.; Randles, Ronald H.

Biometrika 89, No. 4, 851-860 (2002).

Summary: A robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one. The estimator is robust in the sense that it has a bounded influence function, a positive breakdown value and has high efficiency compared to the sample mean for heavy-tailed distributions. Perhaps its greatest strength is that, unlike other affine equivariant multivariate medians, it is easily computed for data in any practical dimension.

MSC:

62H12	Estimation in multivariate analysis
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

bounded influence; breakdown; \(L1\) median; multivariate location estimate; multivariate median; Oja median; robustness