Quantile Regression at Optimal Location and Its Applications

• Activity Number: 182
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yuan Liu*+ and Matteo Bottai
• Companies: Emory University and University of South Carolina
• Keywords: Quantile regression ; Asymmetric Laplace Distrubtion

Abstract

Quantile regression (QR) looks into the relationship at a serial of quantiles of conditional distribution of outcome given predictors. In medical research, data analysis is aimed to answer hypothesis questions, which leads to the query which quantile should be used. In this study, we utilize the natural connection between the three-parameter asymmetric Laplace distribution (ALD) and QR, and show that the maximum likelihood estimator of parameters based on ALD assumption results in a quantile regression at the optimal quantile. The method converges to median regression when the error follows a symmetric distribution, and focuses on a lower/upper quantile when the error is skewed to right/left. In the simulation study, the method is generally more efficient than mean regression for data has skewed or over-dispersed error distribution. An application of the method is illustrated.