Nonparametric regression with nonignorable missing covariates and outcomes using bounded inverse weighting

We consider nonparametric regression where the covariate and the outcome variable are both subject to missingness. Previous work only discussed one of the variables that may be missing, but not both. Since missing at random is not an appropriate assumption in such a nonmonotone missing data context, we shall assume a missing not at random mechanism. We construct an inverse probability weighting local polynomial estimator based on a recently developed nonmonotone missing data model. It is well known that if the inverse probability weighting is too large at some fully observed cases, the resulting estimator would be deteriorated. To overcome this issue, we introduce a constrained maximum likelihood estimation and an estimating equations method to ensure that the resulting weighting is bounded. We prove the asymptotically normal result for the resulting regression estimator. Simulation results show good practical performance of our method. A real data example is also presented.