High-dimensional inference in misspecified linear models

TL;DR

This paper investigates high-dimensional linear models under misspecification, providing valid inference methods like de-sparsified Lasso and discussing robustness and interpretation issues.

Contribution

It offers new interpretations and assumptions for valid inference in misspecified high-dimensional linear models, focusing on the de-sparsified Lasso method.

Findings

Valid asymptotic inference under misspecification

Implications for sample splitting techniques

Enhanced robustness in high-dimensional inference

Abstract

We consider high-dimensional inference when the assumed linear model is misspecified. We describe some correct interpretations and corresponding sufficient assumptions for valid asymptotic inference of the model parameters, which still have a useful meaning when the model is misspecified. We largely focus on the de-sparsified Lasso procedure but we also indicate some implications for (multiple) sample splitting techniques. In view of available methods and software, our results contribute to robustness considerations with respect to model misspecification.