Inverse Probability Weighting for Quantile Regression

• Activity Number: 462
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ben Sherwood*+
• Keywords: Missing Data ; Quantile Regression ; Inverse Probability ; Weighting

Abstract

Quantile regression estimates the conditional quantile of a response. When using linear regression we make parametric assumptions about the errors and assume they are homoscedastic. Quantile regression is robust alternative that makes no parametric assumptions about the errors and allows for heteroscedasticity. While robust to outliers it can be biased by missing data. We examine the case of some covariates are missing and other covariates and the response are fully observed. Inverse probability weighting (IPW) is a technique that has been used to provide consistent estimate in the linear regression setting. We extend IPW to the quantile regression and show that under some regularity conditions it provides a consistent and asymptotically normal estimate of the quantile regression coefficients and that a generalization of BIC can be used for model selection. Simulations are presented to show the performance of IPW.