A Weighted Likelihood Approach Based on Statistical Data Depths

TL;DR

This paper introduces a robust weighted likelihood estimation method using statistical data depths to downweight outliers, demonstrated on multivariate normal models and real data sets.

Contribution

It presents a novel weighted likelihood approach based on data depths for robust parameter estimation, applicable to multivariate models.

Findings

Method provides robust estimates with high efficiency under the true model.

Downweights outliers effectively in multivariate normal estimation.

Illustrated robustness through real data examples.

Abstract

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model with that of the sample in a given point. Observations are considered regular when the ratio of these two depths is close to one, whereas, when the ratio is large the corresponding score contribution may be downweigthed. Details and examples are provided for the robust estimation of the parameters in the multivariate normal model. Because of the form of the weights, we expect that, there will be no downweighting under the true model leading to highly efficient estimators. Robustness is illustrated using two real data sets.