Proposal: DMS 95-05440 PI: Douglas Hawkins Institution: University of Minnesota Title: Diagnostics in Structured Data and Quality Improvement Abstract: The principal directions of the work are case and model diagnostics, and methdologies for handling data with a natural ordering such as time series, or regression data ordered by one of the predictors. The first branch of the work extends methods for identifying atypical cases in multiple regression, multivariate and time series data, and for moderating their effects on the subsequent analysis of the data. The second branch of the work addresses problems of methodologies for identifying structural changes in ordered data (for example regression and multivariate data) and for overcoming the difficulties caused by unknown parameter values. A major application for this work is statistical quality improvement. Many important societal problems involve making valid inferences from complex data sets. The decision whether a facility is adding to the pollution levels in the groundwater, for example, is made on the basis of series of groundwater samples. Analyzing these series is complicated by the presence of apparent maverick values, which may be the result of laboratory error or may reflect actual pollution events. The methods developed with this award help to recognize such values and to resolve the issue of the true pollution levels. Quality improvement is of great importance - both in manufacturing and in all areas of government and the private sector. Pointers to quality improvement for deterioration can be found from identifying structural changes in series of measurements The development of powerful easily-used change diagnostics in this research will lead to sounder and more reliable ways of pinpointing the sources of change. The work has both methodological and computational elements. While the computational aspect benefits from high performance computing equipment and me thods, the development of better computational procedures also leads to solutions to problems currently beyond the powers of even the most powerful computer systems.
