Topics in M-estimation, model selection and modelling

统计模型便于描述观察到的现象。它有助于理解工程学、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方法和理论，以建立基于数据的统计模型，这是对观测数据所表现出的现实的近似。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，关键问题是如何在这些模型中选择最优的近似模型。在选择模型后，可以进行统计分析。需要注意的是，数据的潜在分布可能不像假设的那样，数据可能会受到来自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察和变量。由于验证大数据集的质量是一项艰巨的任务，很难通过人工检查来完成，因此非常需要开发稳健的模型选择程序和稳健的建模技术。如果统计过程抵抗异常值，并且相对于给定分布模型的偏差是稳定的，则该统计过程是稳健的。到目前为止，已经制定了许多强有力的统计程序。基于M-估计的过程在稳健过程的发展中起着重要和互补的作用。根据目前M-估计、模型选择和建模的研究趋势，以下主题被确定为未来的研究重点：统计建模中具有复杂结构和/或高维数据的M-估计或其他基于稳健估计的过程；变点分析；制度切换模型；模型选择和M-估计的一般结果在信号处理和多变量生存分析中的应用。

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.