Corrected-Loss Estimation for Quantile Regression with Covariate Measurement Error

• Activity Number: 482
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Huixia Judy Wang*+ and Leonard A. Stefanski and Zhongyi Zhu
• Companies: North Carolina State University and North Carolina State University and Fudan University
• Keywords: Corrected loss function ; Laplace ; Measurement error ; Normal ; Quantile regression ; Smoothing

Abstract

We study estimation in quantile regression when covariates are measured with error. Existing work in the literature often requires stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicates computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement, and its validity only requires linearity of the particular quantile function of interest. In addition, the proposed method does not require any parametric assumptions on the regression error distributions. We demonstrate with simulation study that the proposed estimators are more efficient than existing methods in various models considered. Finally we illustrate the proposed method through the analysis of a dietary data.