Non- and semi-parametric techniques for handling missing data

Abstract

Missing data arise in various settings, including surveys, clinical trials and epidemiological studies. With or without missing data, the goal of a statistical analysis is to make valid and efficient inferences about a population of interest. The issue of missing values complicates this process. Early on, modelling incomplete data relied on the use of parametric models. Recently, there is a general trend towards non- and semi-parametric approaches to relax assumptions on which parametric models typically rely. Non- and semi-parametric procedures in general will not be as efficient as model-based techniques when there is a posited model, and the model is appropriate. However, if the assumed model is not the correct one, inferences can be worse than useless, leading to misleading interpretations of the data. In this work, a variety of non- and semi-parametric techniques are used to handle missing data problems. The material presented clearly shows the benefits of relaxing assumptions. While starting off with a basic introduction into the field of missing data and non- and semi-parametric techniques, the successive parts of this work focus on different topics. A first part describes a kernel based imputation procedure which makes use of a non-parametric regression relationship between a partially observed response and fully observed covariate. The approach is related to the approximate Bayesian bootstrap method and can be seen as an extension of the local single imputation of Cheng (1994) to a proper local multiple imputation approach. An essential ingredient of the algorithm is the local generation of responses....