Topics in Statistical Modelling and Inference

统计模型有助于理解工程和科学各个领域的系统或过程的结构。统计学中最重要的任务之一是开发方法和理论来建立数据的统计模型。一般来说，这种模式并不是独一无二的。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一个最佳的近似模型。 统计假设经常被用来对数据集进行建模。然而，这些假设可能不成立，数据可能会受到来自各种来源的错误的影响。由于大数据集的质量验证是一项艰巨的任务，很难通过人工检查来完成，因此非常需要开发出能够抵抗离群值并对各种假设的偏差保持稳定的统计建模方法。在这种稳健方法的发展中，M估计或基于方程的估计程序可以发挥重要和补充的作用。 拟议研究的目的是推进统计建模和推断方面的研究。重点是进行理论研究，开发基于M估计和估计方程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、体制转换建模、时空建模、具有复杂结构和/或缺失观测和/或高维的数据的推断等问题。 拟议研究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.