Orthogonalization of multivariate location estimators: The orthomedian

• 成果类型: Article
• 署名作者: Grubel, R
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1457-1473
• 关键词: affine equivariant estimators; matrices

摘要

The coordinatewise median of a multivariate data set is a highly robust location estimator. but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper are introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal transformations. We investigate the asymptotic behavior of this estimator and compare it to the spatial median.