New Rank-Based Estimation Methods for Semiparametric Regression Models

• Activity Number: 622
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Bo Kai*+ and Runze Li and Lan Wang
• Companies: College of Charleston and Penn State University and University of Minnesota
• Keywords: semiparametric modeling ; rank regression ; asymptotic relative efficiency

Abstract

Semiparametric regression modeling has become popular in the recent literature, while its complexity poses new challenges for statistical inference. Most existing procedures are built on least squares estimates, which are sensitive to outliers and inefficient for many non-normal errors. In this work, we propose a new rank-based estimation procedure for semiparametric regression models. The new procedure provides a highly efficient and robust alternative to least squares based methods. The proposed estimates can achieve the optimal convergence rate even when least squares based methods fail due to infinite random error variance. Both the theoretical analysis and extensive numerical simulations reveal that the efficiency gain of the newly proposed estimator over the least squares based estimator can be substantial. In addition, it is shown that the loss in efficiency can be well controlled for estimating both parametric and nonparametric components in the worst case scenario. The proposed procedure can be fast and conveniently implemented using existing R software package.