Variable Selection for Additive Partial Linear Quantile Regression with Missing Covariates

摘要

The standard quantile regression model assumes a linear relationship at thequantile of interest and that all variables are observed. We relax theseassumptions by considering a partial linear model while allowing for missinglinear covariates. To handle the potential bias caused by missing data wepropose a weighted objective function using inverse probability weighting. Ourwork examines estimators using parametric and nonparametric estimates of themissing probability. For variable selection of the linear terms in the presenceof missing data we consider a penalized and weighted objective function usingthe non-convex penalties MCP or SCAD. Under standard conditions we demonstratethat the penalized estimator has the oracle property including cases where$p>>n$. Theoretical challenges include handling missing data and partial linearmodels while working with a nonsmooth loss function and a non-convex penaltyfunction. The performance of the method is evaluated using Monte Carlosimulations and our methods are applied to model amount of time sober forpatients leaving a rehabilitation center.