Mathematical Sciences: Diagnostics and Graphics for Structured Data

该项目将开发数字测量和实时图形程序，用于诊断回归模型、广义线性模型、多变量数据和其他结构化数据。图形方法将结合参数估计和核光滑器，使这些方法有用和直观地超越线性模型的情况。数值病例诊断将基于数据的多个子集，以将对孤立值的敏感性扩展到单个孤立值-简单随机样本情况之外。当通过拟合模型来分析数据时，最重要的任务之一是检查模型的故障以描述数据的行为。对于线性模型，例如多元线性回归模型，无论是数值诊断还是图形诊断，都能成功地识别异常的个体观测或“离群值”。这项研究将为更大的模型组开发诊断，这些模型适合于更高结构或更复杂的情况。

This project will develop numeric measures and real-time graphical procedures for diagnostic use with regression models, generalized linear models, multivariate data and other structured data. Graphical methods will combine parametric estimation and kernel smoothers to make these methods useful and intuitively sensible beyond the linear model case. Numeric case diagnostics will be based on multiple subsetting of the data to extend the sensitivity to outliers beyond the single outlier-simple random sample case. When analyzing data by fitting models, one of the most important tasks is to check for failures of the model to describe the behavior of the data. For linear models, for example multiple linear regression models, both numerical and graphical diagnostics successfully identify aberrant individual observations or "outliers." This research will develop diagnostics for the much larger group of models which are used appropriately for more highly structured or more complicated situations.