Partially Linear Additive Quantile Regression with Missing Covariates

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ben Sherwood*+
• Companies: University of Minnesota
• Keywords: quantile regression ; missing data

Abstract

Quantile regression models the conditional quanitle of a response variable and can provide insight that would be lost by only modeling the conditional mean. Partially linear additive models assume an additive structure that mitigates the curse of dimensionality while allowing for some covariates to have a non-linear relationship with the response. It also assumes a linear relationship for some covariates which can provide for easy interpretation for a select group of covariates. This can be particularly useful when the main covariate of interest is a treatment variable. Missing data is a common problem in data analysis, but little work has been done on how to handle missing data for the quantile regression model. We assume a missing at random structure where some covariates are missing and their missing rate depends on fully observed covariates and the response. If the records with missing data were ignored this would result in asymptotically biased estimates. We propose an inverse probability weighting solution that provides consistent estimates of the unknown non-linear functions and asymptotically normal estimates for the coefficients of the linear covariates.