Struct TylerFit 

pub struct TylerFit { /* private fields */ }

A fitted Tyler shape estimate.

Tyler estimates shape only: shape is normalized to unit determinant and carries no scale. A consequence is that its Mahalanobis distances are correct for ranking observations but are not χ²_p-calibrated; for N(0, Σ) data their squared distances are the Gaussian χ²_p distances times the unidentified factor det(Σ)^{1/p} (so the distances themselves scale by det(Σ)^{1/(2p)}) and for non-Gaussian elliptical data the χ² shape does not apply at all. TylerFit therefore does not implement RobustScatter and offers no default Gaussian outlier map, mirroring how the regression LtsFit declines the ρ-derived efficiency it cannot report. Rank with distances, or opt in explicitly via outliers_assuming_chi2_radial.

Implementations

impl TylerFit

pub fn location(&self) -> &Array1<f64>

The robust centre μ̂ (the supplied location, or the coordinatewise median).

pub fn shape(&self) -> &Array2<f64>

The unit-determinant shape matrix V̂ (det V̂ = 1; no scale identified).

pub fn distances(&self) -> &Array1<f64>

Robust Mahalanobis distances from the shape. Correct for ranking observations, but not χ²_p-calibrated (the scale is unidentified).

pub fn outliers_assuming_chi2_radial(&self, quantile: f64) -> Vec<bool>

Flag outliers by comparing the Tyler distances to the Gaussian cutoff √χ²_{p, quantile}.

As the name says, this assumes a χ²-radial model (e.g. Gaussian) (the assumption Tyler’s shape estimate exists to avoid) and disregards the unidentified squared-distance factor det(Σ)^{1/p}, so the cutoff is meaningful only under that model. It is an opt-in for the Gaussian case; for distribution-free use, threshold distances directly. An empirical quantile flags a fixed proportion of points (≈ 1 − quantile) whether or not any are outliers, unlike this absolute χ² cutoff, which flags ≈ none of clean Gaussian data.

Trait Implementations

impl Clone for TylerFit

fn clone(&self) -> TylerFit

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for TylerFit

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.