Estimation and inference for quantile partially linear varying coefficients models with missing observations

This paper considers estimation and inference for quantile partially linear varying coefficients models, where some of the observations are missing at random. The unknown parameters are estimated using two different two step procedures, one of which is based on iteration and the other is based on profiling. Both procedures are based on inverse probability weighting, where the weights can be estimated either parametrically or nonparametrically. The paper proposes two computationally simple resampling techniques that can be used to consistently estimate the asymptotic distributions and the asymptotic variances of the unknown finite dimensional parameters estimators. For inference, the paper proposes new test statistics for both the finite and infinite dimensional parameters, including a test for constancy of the varying coefficients part of the model. Monte Carlo simulations show that the proposed estimators and test statistics have good finite sample properties. Finally, the paper contains a real data application.