Rank regression under possible model misspecification

Rank regression offers a valuable alternative to the classical least squares approach. The use of rank regression not only provides protection against outlier contamination but also leads to substantial efficiency gain in the presence of heavier-tailed errors. This article studies the asymptotic performance of rank regression with Wilcoxon scores when the regression function is possibly mis-specified. We establish that under general conditions, the Wilcoxon rank regression estimator converges in probability to a well-defined limit and has an asymptotic normal distribution. We also derive a formula for the bias of omitted variables. Besides furthering our understanding of the properties of rank regression, these theoretical results have important implications for developing rank-based model selection and model checking procedures.