Mathematical Sciences: Diagnostics and Graphics for Structured Data

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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.