Elegant robustification of sparse partial least squares by robustness-inducing transformations

Abstract

Robust alternatives exist for many statistical estimators. State-of-the-art robust methods are fine-tuned to optimize the balance between statistical efficiency and robustness. The resulting estimators may, however, require computationally intensive iterative procedures. Recently, several robustness-inducing transformations (RIT) have been introduced. By merely applying such transformations as a preprocessing step, a computationally very fast robust estimator can be constructed. Building upon the example of sparse partial least squares (SPLS), this work shows that such an approach can lead to performance close to the computationally more intensive methods. This article proves that the resulting estimator is robust, by showing that it has a bounded influence function. To establish the latter, this article is first to formulate SPLS at the population level and therefrom, to derive (classical) SPLS's influence function. It also shows that the breakdown point of the resulting regression coefficients can approach 50% when properly tuned. Extensive Monte Carlo simulations highlight the advantages of the new method, which performs comparably and at times even better than existing robust methods based on M-estimation, yet at a significantly lower computational burden. Two application studies related to the cancer cell panel of the National Cancer Institute and the chemical analysis of archaeological glass vessels further support the applicability of the proposed robustness-inducing transformations, combined with SPLS.