Fitting Generalized Multivariate Huber Loss Functions

In this letter, we consider a class of generalized multivariate Huber (GMH) loss functions. Our goal is parameter estimation in linear models contaminated by non-Gaussian noise. We assume access to a secondary dataset of independent noise realizations, and we use these data to fit a convex GMH function that will then lead to efficient parameter estimation. Our framework includes the classical weighted least squares and Huber's function as special cases. We demonstrate its advantages in heavy-tailed noise distributions.