Nearly minimax robust estimator of the mean vector by iterative spectral dimension reduction

Understand

We study the problem of robust estimation of the mean vector of a sub-Gaussian distribution.

• We introduce an estimator based on spectral dimension reduction (SDR) and establish a finite sample upper bound on its error that is minimax-optimal up to a logarithmic factor.
• Furthermore, we prove that the breakdown point of the SDR estimator is equal to $1/2$, the highest possible value of the breakdown point.
• In addition, the SDR estimator is equivariant by similarity transforms and has low computational complexity.