The first of three components to the proposed research exploits the form of weighted least squares estimators to develop new approaches to regression diagnostics, robust estimation, and variable selection. The second component addresses the problem of frequentist inference after model averaging, and "bagging" in particular. A new "parallel bootstrap" resampling approach is proposed for finding variance estimators with total computational effort about twice that of the original bagging step. The third component addresses the problem of determining when model averaging is beneficial. Model averaging often improves prediction over a base procedure, but not always. Because the improvement in prediction is achieved at the expense of interpretability, it is important to know when model averaging is advantageous and when it is not. Thus a model-stability index that is applicable to general regression models will be developed and studied.
The proposed research addresses well-recognized problems that arise when estimating the relationship between a dependent response variable Y and several predictor variables, e.g., Y = loan failure and X1 = household income, X2 = number of dependents, etc. The methods and insights developed by this research will be very useful in applications of regression modeling and thus will facilitate research in numerous other disciplines including basic science research and applied research that directly affects quality of life. Results will be disseminated via web and journal publications, conferences, and seminars. The project will also significantly impact human resource development in the guise of education and training of graduate students, some of whom who are likely to come from under-represented groups in light of the NC State Statistics Department's commitment to a diverse graduate program.
