Topics in M-estimation, model selection and modelling

统计模型便于表示观察到的现象。它有助于理解工程、自然科学和社会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用于构建基于数据的统计模型的方法和理论，该模型是对观察到的数据中显示的现实的近似。这样的模式一般来说并不独特。对于给定的一组竞争模型，关键问题是如何在其中选择最佳近似模型。在选定模型后，可进行统计分析。请注意，数据的基本分布可能与假设的不同，数据可能会受到各种来源的误差的影响。在这个数据丰富的时代，数据往往包含许多观测和变量。由于验证大型数据集的质量是一项艰巨的任务，并且很难通过人工检查完成，因此非常需要开发鲁棒的模型选择程序和鲁棒的建模技术。如果一个统计程序对离群值有抵抗力，并且在偏离给定分布模型方面是稳定的，则该统计程序是稳健的。到目前为止，已经开发了许多强大的统计程序。基于M-估计的方法在稳健方法的发展中起着重要的补充作用，根据目前M-估计、模型选择和建模的研究趋势，提出了以下几个值得进一步研究的课题：统计建模中复杂结构和/或高维数据的M-估计或其他稳健估计方法;变点分析;状态转换模型;一般结果在信号处理和多变量生存分析中的模型选择和M-估计的应用。

A statistical model is convenient for representing the observed phenomenon. It contributes to the understanding of the structure of a system or a process in various fields of engineering and natural and social sciences. One of the most important tasks in statistics is to develop methodologies and theories for constructing a statistical model based on data, which is an approximation to the reality manifested in the observed data. Such a model is not unique in general. For a given set of competing models, the key issue is then how to choose the best approximating model among them. After a model is chosen, statistical analysis may be performed.It is noted that the underlying distribution of data may not be as assumed and the data are subject to error from various sources. In this data-rich era, data often contain many observations and variables. Since verifying the quality of a large dataset is a formidable task and is hardly  done by manual inspection, there are great needs to develop robust model selection procedures and robust modelling techniques. A statistical procedure is robust if it is resistant to outliers and stable in respect to deviations from a given distributional model. Many robust statistical procedures have been developed so far. M-estimation based procedures play important and complementary roles in the development of robust procedures.On the basis of current research trend on M-estimation, model selection and modelling, the following topics have been identified to be of great interests for future study: the M-estimation or other robust estimation based procedures for data with complex structure and/or high dimensionality in statistical modelling; changepoint analysis; regime-switching models; the applications of the general results on model selection and M-estimation in signal processing and multivariate survival analysis.