For a p-dimensional data set of size np+1 in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Affine equivariance
- Robust multivariate statistics
- Sparse data