Robust specification testing for rank-based linear regression

Abstract This paper introduces a robust specification test for linear regression built on a rank-score empirical process. The proposed test is distribution-free, easy to implement, and accommodates a broad class of score functions. We derive the asymptotic properties of the test statistics under the null, fixed alternatives, and a sequence of local alternatives. To implement the test in finite samples, we employ a simple multiplier bootstrap procedure with establishing its asymptotic validity. Simulations and an empirical application indicate reliable size and strong power with notable robustness to heavy-tailed errors and outliers.