Quantile Regression for Time-Varying Coefficient Longitudinal Model

• Activity Number: 232
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Seonjin Kim*+ and Zhibiao Zhao
• Companies: Penn State University and Penn State University
• Keywords: Asymptotic efficiency ; Bandwidth selection ; Longitudinal model ; Nonparametric smoothing ; Quantile regression ; Time-varying coefficient.

Abstract

For nonparametric estimation of time-varying coefficient longitudinal models, the widely used local least-squares smoothing uses information from the local sample average. Motivated by the fact that a combination of multiple quantiles is more informative than the local sample average, we investigate quantile regression based methods by combining information across multiple quantiles. When the quantile information is optimally combined, the asymptotic variance of the estimators attains the optimal Cramer-Rao bound. We also study estimators by sub-optimally combining quantile information using the uniform weights, inverse of variance weights, and thresholding weights. Fully data-driven bandwidth selection and optimal weights estimation are implemented through a two step procedure. Monte Carlo simulation studies show that, for non-normal distributions, the proposed methods significantly outperform the local least-squares method; for normal distribution, they have comparable performance. We use the Six Cities Study of Air Pollution and Health to illustrate the new methodology.