Valid Inference After Selecting Predictors and Variable Transformations

• Activity Number: 434
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Andreas Buja*+ and Lawrence Brown and Linda Zhao and Richard Berk and Edward George
• Companies: Wharton School and Wharton School and Wharton School and University of Pennsylvania and Wharton School
• Keywords: variable selection ; model selection ; Box-Cox transformations ; variable transformations

Abstract

Common practice in model fitting is (1) to select predictors based on one of the many popular predictor selection procedures, and (2) to transform the response and possibly the predictors with logarithms, square roots or more generally Box-Cox transforms. Recent research has attempted to address the problem of obtaining valid statistical inference after variable selection. In the present talk we address the larger and more realistic problem of allowing variable transformations as well. An issue that needs to be resolved before even attempting to address inference after (1) and (2) is the necessity of valid statistical inference in misspecified models. Thereafter we examine a procedure that has the promise of producing valid inference after predictor selection as well as selection from a finite vocabulary of variable transformations.