Regression quantiles and their two-step modifications

Abstract

Regression quantiles and their two-step modifications based on R-estimation of slope components of regression parameter are asymptotically equivalent and are very close numerically even for small sample sizes; their extreme versions even exactly coincide. Regarding that, we study their relations under finite samples and show under which conditions their values exactly coincide.

This inter-relation is also numerically illustrated.

Keywords

• RANK-SCORES
• AUTOREGRESSION
• REGRESSION QUANTILE
• REGRESSION RANK SCORES
• TWO-STEP REGRESSION QUANTILE
• AUTOREGRESSION QUANTILE
• R-ESTIMATOR