Dimension-reduced Estimation with Nonignorable Nonresponse

To estimate population parameters of a response variable when the data having nonignorable nonresponse and the dimension of covariate is not low, we consider the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To solve the identifiability problem, we use an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates. Three different nonparametric/semiparametric estimation methods are proposed based on inverse probability weighting, mean imputation, and augmented inverse probability weighting. To improve the efficiency and alleviate the curse of dimensionality, we apply sufficient dimension reduction technique to produce efficient kernel estimation and then obtain dimension reduced estimators. Consistency and asymptotic normality of the proposed estimators are established. We further show that these estimators are asymptotically equivalent. The finite-sample performance of the estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.