Topics in M-estimation, model selection and modelling

M 估计、模型选择和建模主题

• 批准号: 105557-2007
• 负责人: Wu, Yuehua
• 金额: $ 1.6万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=361170
• 关键词: Topics; estimation; model; selection; modelling

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.

统计模型便于表示所观察到的现象。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。统计学最重要的任务之一是发展基于数据的统计模型的方法和理论，统计模型是对观察到的数据所体现的现实的近似。一般来说，这种模式并不是唯一的。对于给定的一组相互竞争的模型，关键问题是如何从中选择最佳的近似模型。选择模型后，可以进行统计分析。值得注意的是，数据的基本分布可能不像假设的那样，数据可能受到来自各种来源的误差的影响。在这个数据丰富的时代，数据通常包含许多观察值和变量。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，因此非常需要开发稳健的模型选择程序和稳健的建模技术。如果统计程序能够抵抗异常值，并且在偏离给定分布模型方面保持稳定，那么它就是稳健的。到目前为止，已经开发了许多可靠的统计程序。基于m估计的程序在稳健程序的开发中起着重要的补充作用。基于目前对m估计、模型选择和建模的研究趋势，确定了以下主题是未来研究的重要方向：统计建模中对复杂结构和/或高维数据的m估计或其他基于鲁棒估计的程序；changepoint分析;状态变换模型;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。