Topics in Statistical Modelling and Inference

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A statistical model contributes to the understanding of the structure of a system or a process in various fields of engineering and sciences. One of the most important tasks in statistics is to develop methodologies and theories to build a statistical model for data. Such a model is not unique in general. For a given set of competing models, the key issue is then how to select a best approximating model from these models. Statistical assumptions are often made to model a data set. However these assumptions may not hold and the data are subject to error from various sources. Since quality verification of a large data set is a formidable task and is hardly done by manual inspection, there are great needs to develop statistical modelling methods that are resistant to outliers and stable in respect to deviations from various assumptions. In the development of such robust methods, M-estimation or estimating equation-based procedures can play important and complementary roles. The objective of the proposed research is to advance the study in statistical modelling and inference. The emphasis is put on performing theoretical investigations, and developing M-estimation and estimating equation-based procedures as well as fast computational algorithms to tackle the problems in model selection, change-point analysis, cluster analysis, regime-switching modelling, spatio-temporal modelling, inference for data that have complex structure and/or missing observations and/or high dimensionality. The advancements achieved under the proposed research will produce significant impact in statistical modelling and inference, and their applications in practice.