Module multivariate 

Multivariate robust statistics: robust estimates of multivariate location and scatter and the outlier detection built on them.

The organizing object here is a location–scatter pair (μ̂, Σ̂) (a robust centre and a robust covariance) from which a robust Mahalanobis distance dᵢ = √((xᵢ − μ̂)ᵀ Σ̂⁻¹ (xᵢ − μ̂)) flags multivariate outliers, just as robust residuals flag them in regression. Four estimators produce such a pair, trading efficiency against breakdown and equivariance:

• Mcd: the Minimum Covariance Determinant (Rousseeuw 1985) via FAST-MCD (Rousseeuw & Van Driessen 1999): 50%-breakdown, affine-equivariant, the multivariate analogue of LTS.
• Ogk: the Orthogonalized Gnanadesikan–Kettenring estimator (Maronna & Zamar 2002): a fast, deterministic, positive-definite pairwise estimator (orthogonally, not fully affine, equivariant).
• MScatter: a monotone M-estimator of location and scatter (Maronna 1976): the direct multivariate analogue of the regression M-estimator, reusing a robust_rs_core::rho::RhoFunction weight.
• Tyler: Tyler’s (1987) distribution-free M-estimator of shape, normalized to unit determinant.

mahalanobis exposes the distance/outlier map over any (μ̂, Σ̂) pair, together with the classical (non-robust) mean/covariance baseline.

Modules

mahalanobis

Robust Mahalanobis distances and the multivariate outlier map, over any robust location/scatter pair (μ̂, Σ̂), plus the classical (non-robust) mean/covariance baseline they are meant to replace.

Structs

MScatter

A configured monotone M-estimator of location and scatter, generic over the RhoFunction weight (default Huber, k = 1.345).

Mcd

A configured FAST-MCD estimator.

McdFit

A fitted Minimum Covariance Determinant estimate.

Ogk

A configured OGK estimator, generic over the robust univariate scale (the default Qn is Maronna & Zamar’s recommendation; the location functional paired with it is the median).

ScatterFit

A fitted robust location–scatter estimate.

Tyler

A configured Tyler shape estimator.

TylerFit

A fitted Tyler shape estimate.

Traits

RobustScatter

Quantities every fitted robust covariance estimator can report, the multivariate counterpart of crate::estimator::RobustEstimator.