Robust Estimation in High Dimensional Generalized Linear Models

TL;DR

This paper introduces a deterministic robust initial estimate for high-dimensional generalized linear models, improving robustness and computational feasibility over traditional subsampling methods.

Contribution

It proposes a novel deterministic initialization method for M-estimators in high-dimensional GLMs, based on transformations, with an iterative algorithm for robust estimation.

Findings

The new method performs well in Monte Carlo experiments.

It reduces the computational burden compared to subsampling approaches.

The approach enhances robustness in high-dimensional settings.

Abstract

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust procedures are presented in the literature but they need a robust initial estimate in order to be computed. This is especially important for robust procedures with non convex loss function such as redescending M-estimators. Subsampling techniques are often used to determine a robust initial estimate; however when the number of unknown parameters is large the number of subsamples needed in order to have a high probability of having one subsample free of outliers become infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. Based on ideas in Pena and Yohai (1999), we introduce a deterministic robust initial estimate for M-estimators based on transformations Valdora and Yohai (2014) for which we also develop an iteratively reweighted least squares algorithm. The new methods are studied by Monte Carlo experiments.