# Weighted likelihood estimation of multivariate location and scatter

## TL;DR

This paper introduces a new weighted likelihood estimation method for multivariate location and scatter that uses Mahalanobis distances for weighting, improving robustness and avoiding high-dimensional density estimation issues.

## Contribution

It proposes a Mahalanobis distance-based weighting scheme for weighted likelihood estimation, enhancing robustness and computational efficiency in multivariate analysis.

## Key findings

- Effective outlier detection rules developed
- Robust dimensionality reduction techniques introduced
- Method demonstrated through numerical and real data studies

## Abstract

A novel approach to obtain weighted likelihood estimates of multivariate location and scatter is discussed. A weighting scheme is proposed that is based on the distribution of the Mahalanobis distances rather than the distribution of the data at the assumed model. This strategy allows to avoid the curse of dimensionality affecting non-parametric density estimation, that is involved in the construction of the weights through the Pearson residuals Markatou et al (1998). Then, weighted likelihood based outlier detection rules and robust dimensionality reduction techniques are developed. The effectiveness of the methodology is illustrated through some numerical studies and real data examples.