Affine equivariant rank-weighted L-estimation of multivariate location

TL;DR

This paper introduces a new class of robust, affine-equivariant L-estimators for multivariate location that leverage Mahalanobis distances, with a focus on their computational aspects.

Contribution

It proposes a novel class of affine-equivariant L-estimators for multivariate location, emphasizing their robustness and computational implementation.

Findings

Establishes affine-equivariance of the estimators

Provides iterative algorithms for computation

Demonstrates robustness through numerical examples

Abstract

In the multivariate one-sample location model, we propose a class of flexible robust, affine-equivariant L-estimators of location, for distributions invoking affine-invariance of Mahalanobis distances of individual observations. An involved iteration process for their computation is numerically illustrated.