= Solution
The <coordinatewise median> suffers a contamination error of order $\epsilon\sqrt d$ with constant probability. In contrast, the <Tukey median> under an isotropic Gaussian model satisfies a high-probability Euclidean error bound of order
$$
\epsilon+\sqrt{\frac dn}+\sqrt{\frac{\log(1/\delta)}n}
$$
with probability at least $1-\delta$, up to universal constants. Its contamination term is dimension-free. Thus coordinatewise estimation loses a factor $\sqrt d$ in its dependence on adversarial contamination.
Back to article page
