Topics in Statistical Modelling and Inference

统计模型有助于理解工程和科学各个领域中的系统或过程的结构。统计学中最重要的任务之一是发展方法和理论来建立数据的统计模型。这样的模式一般来说并不独特。对于给定的一组竞争模型，关键问题是如何从这些模型中选择最佳近似模型。 统计假设通常用于对数据集进行建模。然而，这些假设可能不成立，数据可能会受到各种来源的误差的影响。由于大型数据集的质量验证是一项艰巨的任务，并且很难通过人工检查完成，因此非常需要开发能够抵抗离群值并且在偏离各种假设的情况下稳定的统计建模方法。在这种稳健方法的开发中，M-估计或基于估计方程的程序可以发挥重要的补充作用。 拟议研究的目的是推进统计建模和推断的研究。重点是进行理论研究，并开发M-估计和估计方程为基础的程序，以及快速计算算法，以解决模型选择，变点分析，聚类分析，政权切换建模，时空建模，推理的数据，具有复杂的结构和/或丢失的观测和/或高维的问题。 在拟议的研究中取得的进展将对统计建模和推断及其在实践中的应用产生重大影响。

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.