Soft Maximin Estimation for Heterogeneous Data

TL;DR

This paper introduces soft maximin estimation, a flexible and computationally efficient method for extracting robust signals from heterogeneous data, balancing pooled and maximin approaches with theoretical guarantees and practical implementation.

Contribution

It proposes the soft maximin estimator, which interpolates between pooled and maximin estimation, with theoretical properties and an R package implementation.

Findings

Soft maximin improves predictive performance over pooled OLS and maximin.

The method is computationally efficient and scalable.

Empirical results demonstrate advantages on real and simulated data.

Abstract

Extracting a common robust signal from data divided into heterogeneous groups can be difficult when each group -- in addition to the signal -- can contain large, unique variation components. Previously, maximin estimation has been proposed as a robust estimation method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive alternative aimed at striking a balance between pooled estimation and (hard) maximin estimation. The soft maximin method provides a range of estimators, controlled by a parameter $\zeta>0$, that interpolates pooled least squares estimation and maximin estimation. By establishing relevant theoretical properties we argue that the soft maximin method is both statistically sensibel and computationally attractive. We also demonstrate, on real and simulated data, that the soft maximin estimator can offer improvements over both pooled OLS and hard maximin in terms of predictive performance and computational complexity. A time and memory efficient implementation is provided in the R package \verb+SMME+ available on CRAN.