POWRE: Exploratory research in the interface of robustness/mixtures

所有稳健性方法的共同基本主题是构建在假定的参数模型附近表现良好的统计程序。在这种情况下，统计建模的拟合优度不再相关。所有这些方法的另一个问题是，统计方法是为位置尺度模型开发的，不容易扩展到其他类型的模型。我将探索参数估计中稳健理论的发展，该理论解决了上述两个问题，并且在计算上易于使用。新理论将解决混合模型、线性回归、Logistic回归的理论和应用中出现的稳健性问题，以及一般在广义线性模型的应用中出现的稳健性问题。我的方法的基础在Markatou、Basu和Lindsay(1997、1998)的联合论文以及Lindsay(1994)的论文中概述。新方法的稳健性将通过经典工具(如分解)和较不传统的工具(如相应估计方程的稳定性)进行研究。该POWRE项目由MPS多学科活动办公室(OMA)和数学科学司(DMS)共同支持。

The common underlying theme of all approaches to robustness is the construction of statistical procedures that perform well in the neighborhood of the assumed parametric model. In this context, the goodness of fit aspect of statistical modeling is no longer relevant. Another problem with all these approaches is that statistical methods are developed for the location-scale models and are not easily extended to other types of models. I will explore the development of a robust theory in parametric estimation that addresses the above two problems and it is computationally easy to use. The new theory will address robustness problems that arise in the theory and application of mixture models, linear regression, logistic regression and generally in the application of generalized linear models. The basis for my approach is outlined in the joint papers by Markatou, Basu and Lindsay (1997, 1998) and the paper by Lindsay (1994). The robustness of the new methodology will be studied via classical tools (such as breakdown) and via less traditional tools (such as stability of the corresponding estimating equations). This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).