Sufficient dimension reduction and instrument search for data with nonignorable nonresponse

Consider a response variable subject to nonignorable nonresponse and a fully observed covariate vector. The purpose of our study is threefold. First, we study how to extend nonparametric sufficient dimension reduction to data with nonignorable nonresponse. Second, we utilize sufficient dimension reduction to search an instrument, a linear function of covariates that is related to the response variable but can be excluded from the propensity of nonignorable nonresponse, for the purpose of identifying unknown parameters in a semiparametric propensity and a nonparametric distribution of response variable and covariates. Third, we establish asymptotic results for parameter estimators based on sufficient dimension reduction and instrument search, and investigate the effect on the limiting distribution of parameter estimators due to instrument search. We evaluate the performance of proposed estimators in a Monte Carlo study and illustrate our method in an application to AIDS Clinical Trials Group Protocol 175 data.