| Summary: | In many longitudinal studies, several longitudinal processes may be associated. For example, a time-dependent covariate in a longitudinal model may be measured with errors or have missing data, so it needs to be modeled together with the response process in order to address the measurement errors and missing data. In such cases, a joint inference is appealing since it can incorporate information of all processes simultaneously. The joint inference is not only more efficient than separate inferences but it may also avoid possible biases. In addition, longitudinal data often contain outliers, so robust methods for the joint models are necessary. In this thesis, we discuss joint models for two correlated longitudinal processes with measurement errors, missing data, and outliers. We consider two-step methods and joint likelihood methods for joint inference, and propose robust methods based on M-estimators to address possible outliers for joint models. Simulation studies are conducted to evaluate the performances of the proposed methods, and a real AIDS dataset is analyzed using the proposed methods. === Science, Faculty of === Statistics, Department of === Graduate
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