Fully nonparametric inverse probability weighting estimation with nonignorable missing data and its extension to missing quantile regression

In practical data analysis, the not-missing-at-random (NMAR) mechanism is typically more aligned with the natural causes of missing data. The NMAR mechanism is complicated and adaptable, surpassing the capabilities of classical methods in addressing this missing data challenge. A comprehensive analysis framework for the NMAR problem is established, and a novel inverse probability weighting method based on the fully nonparametric exponential tilting model and sieve minimum distance is constructed. Additionally, given the broad field of applications for the quantile regression model, fully nonparametric inverse probability weighting and augmented inverse probability weighting for estimating quantile regression under NMAR are introduced. Simulation studies demonstrate that the proposed methods are better suited for various flexible propensity score functions. In practical applications, our methods are applied to the AIDS Clinical Trials Group Study 175 data to examine the effectiveness of treatments on HIV-infected subjects.