Weighted rank estimation for nonparametric transformation models with nonignorable missing data

Abstract

Abstract Missing data occur in almost every field and a great deal of literature has been established for the analysis of missing data with different types of missing mechanisms and under various models. Nonignorable missing data can be analyzed using nonparametric transformation models, which has not been discussed in the literature. In particular, assume that the conditional response probability can be written as the product of separate unknown functions of the response variable and covariates, respectively. For estimation of regression parameters, a weighted rank (WR) estimation procedure is proposed and the asymptotic properties of the resulting WR estimator are established. For the determination of the proposed estimator, a simple coordinate-wise optimization algorithm is developed, and a numerical study is conducted for assessing the performance of the proposed approach and suggests that it works well in practice. An illustration is also provided.