Statistical Modelling and Inference with Complex Data

从自然科学到工程学、卫生科学、人文科学和社会科学等领域的研究都极大地受益于统计科学。然而，许多常用的推断程序（在流行的统计软件包中构成了大多数技术）假设数据是理论上理想的格式，例如，独立和相同分布的观测值的集合。不幸的是，这种假设在现实生活的研究中往往是不现实的，因此对输出的传统解释可能会产生误导。一些研究人员观察到，他们的数据结构复杂，使现有的统计工具失效，但他们没有其他方法。

Studies in fields ranging from natural sciences to engineering to health sciences to human and social sciences have benefited greatly from the statistical sciences. However, many commonly used inferential procedures, which form the majority of the techniques implemented in popular statistical software packages, assume that the data are in a theoretically ideal format, e.g., a collection of independent and identically distributed observations. Unfortunately, this assumption is often not realistic in real-life studies, and thus conventional interpretations of the output can be misleading. Some researchers have observed that the complex structures of their data invalidate existing statistical tools, but they do not have alternative approaches. The broad objective of this proposed research program is to develop new methodology for statistical modelling and inference to circumvent the challenges and limitations of conventional statistical tools in the context of complex data. Our three focal points are efficiency, robustness, and feasibility. The specific aims of this proposal are (1) to propose new models and approaches for coarsened event times using readily available longitudinal information; (2) to investigate regression analysis with time-dependent covariates in the presence of incomplete covariate information; and (3) to develop new formulation and analysis procedures for longitudinal observations subject to informative inspection. All the statistical problems are formulated based on real-life projects; specialized procedures will be developed to address particular challenges in applications. Statistical models are powerful tools that offer researchers a deep understanding of complex systems and the ability to make predictions. Adapting the framework developed in my recent NSERC-funded research program, we will utilize information from application areas to build relevant models and conduct scientifically meaningful analyses. Training HQPs and disseminating the research results are two important aspects of the proposed research. Students will participate in the whole range of research activities including the literature review, statistical formulation, asymptotic derivation, simulation, and practical data analysis. We will develop software packages to make the research accessible to statistical practitioners when the research is sufficiently mature. We anticipate that the proposed research will contribute to statistical theory and practice by providing feasible, efficient, and robust approaches, and that the associated training will produce highly qualified statisticians.