Model Diagnostics for Quantile Regression

• Activity Number: 411
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guixian Lin*+ and Huixia Judy Wang
• Companies: SAS Institute Inc. and North Carolina State University
• Keywords: Quantile regression ; Model misspecification ; Goodness of fit ; Inference of quantile regression process ; Empirical process ; Residuals plots

Abstract

Quantile regression is emerging as an attractive alternative method to the ordinary least squares regression, and has been widely used in practice. It is very powerful in analyzing data with heterogeneity, and is particularly useful in detecting evolving covariate effects along the quantiles. For example, in medical studies, we might be interested in detecting heterogeneous treatment effects concentrated in the upper tails. To make valid and efficient inferences in such situations, we need to test model adequacy for a rang of quantiles instead of a particular quantile. Here we propose a test based on the cumulative sums process of the residuals. The two key advantages of the proposed method are: 1. nonparametric smoothing is not involved; 2. plots of the cumulative residual processes can identify the nature of model misspecification. The asymptotic properties of of the test statistic are derived. Simulation results demonstrate the satisfactory performance of the proposed test in finite sample size according to its power and size.