Linear Modal Regression with Errors in Variables

• Activity Number: 164 - Random and Mixed Effect Models
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Xiang Li* and Xianzheng Huang
• Companies: University of South Carolina and University of South Carolina
• Keywords: Corrected Score ; Kernel ; Measurement Error ; Monte Carlo

Abstract

We consider modal regression in the presence of measurement error. Empirical evidence suggests that ignoring measurement error can result in inconsistence inference on regression coefficients. To account for measurement error, we adopt the Monte Carlo corrected score method (Novick and Stefanski, 2002) to numerically approximate an unbiased sore function based on which we estimate the regression parameters consistently. To relax the normality assumption on measurement error required for the validity of Monte Carlo corrected score, we propose a second method where we analytically construct a corrected score using the deconvoluting kernel (Stefanski and Caroll, 1990). We rigorously study the asymptotic properties of corrected score estimators resulting from the second method. Numerical evidence from simulation study and a real-life application to dietary data suggest that the two proposed methods yield estimators that substantially outperform the naive estimator.