Tight breakdown bound for the axis-augmented estimator

Derive a tight contamination-breakdown bound for the full Wand anomaly estimator that combines the rotation-equivariant uniform-sphere pathway with the fixed axis-aligned pathway.

Background

The paper proves a breakdown guarantee of at least 1/(d+1) for Wand’s uniform-sphere pathway by combining the per-direction median/MAD statistic with Tukey halfspace-depth reasoning. The complete estimator, however, also includes a fixed axis-aligned pathway designed to detect single-feature anomalies. Because this pathway is not affine-equivariant, the composition argument used for the uniform-sphere pathway does not directly apply, leaving the robustness of the mixed estimator unresolved.