Robust Covariance / Elliptic Envelope

Best for: Gaussian-like data

How it works

Fits a Gaussian (elliptic) envelope but estimates location and scatter with the Minimum Covariance Determinant, the $h$-point subset whose covariance determinant is smallest, making $\hat\mu$ and $\hat\Sigma$ resistant to the very outliers being sought. Points are scored by the robust Mahalanobis distance $d^2(x)=(x-\hat\mu)^\top\hat\Sigma^{-1}(x-\hat\mu)$, which follows a $\chi^2_p$ distribution under normality, so a quantile cutoff defines the boundary. Works well when inliers are roughly Gaussian but breaks down for multimodal data.

Common fields

Risk modeling · industrial monitoring