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Abstract:
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Missing data is rampant in data sets in every field of science. In the past few decades, there has been interest in understanding the underlying pattern of missingness, formally known as the missingness mechanism. There are two main types of missingness mechanisms: Ignorable and Nonignorable. Most likelihood or imputation-based methods developed assume the ignorable condition, which is the more well studied condition. We discuss the nonignorable condition which is less well studied. It is the hardest to deal with but also the most likely to occur. Under the nonignorable missingness assumption, the missing response depends on a set of covariates and the value of the response itself. We model the missingness mechanism by a partially parametric logistic relation where the dependence on covariates is unspecified. We propose a general class of estimators for the model parameters and also functional estimation, including estimating the mean response and response quantiles. The resulting estimators are shown to be robust through theoretical derivations and simulations.
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