A correlation-robust shrinkage estimator: Oracle inequality and an application on out-of-sample factor selection

Abstract

Shrinkage methods are widely used in big data to achieve sparse variable selection and reduce overfitting. However, these methods, such as LASSO (Tibshirani, 1996), often struggle when faced with highly correlated predictors. In this paper, we examine a recently developed machine learning estimator that is robust to highly correlated variables, providing superior out-of-sample performance compared to traditional shrinkage techniques. We establish the asymptotic properties of this estimator under general conditions, including i.i.d. sub-Gaussianity. Empirically, we demonstrate the practical benefits of this approach in selecting factors to construct hedged portfolios, achieving significantly higher Sharpe ratios compared to benchmarks such as LASSO, Ridge, and Elastic Net in an out-of-sample context.