On the distance between mean and geometric median in high dimensions
Abstract
The geometric median, a notion of “center” for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results.
Fields of Study & Subjects
Digital Image Processing Techniques
Morphological variations and asymmetry
Statistical and numerical algorithms
Publication details
- Journal / source
- Statistics & Probability Letters
- Volume
- 233
- Pages
- 110679–110679
- Publication date
- 6 February 2026
- Language
- EN