SCAD penalized rank regression with a diverging number of parameters

In this paper, we study the robust variable selection and estimation based on rank regression and SCAD penalty function in linear regression models when the number of parameters diverges with the sample size increasing. The proposed method is resistant to heavy-tailed errors or outliers in the response, since rank regression combines properties of least absolute deviation (LAD) and least squares (LS), which is generally more robust and efficient than the LS and LAD estimators, respectively. Furthermore, when the dimension pn of the predictors satisfies the condition pnlogn/n→0, as n→+∞, where n is the sample size, and the tuning parameter is chosen appropriately, the proposed estimator can identify the underlying sparse model and have desired large sample properties including n/pn consistency and asymptotic normality. Some simulation results confirm that the newly proposed method works very well compared to other existing methods.