Avoiding Extrapolation in High-Dimensional Prediction Space with Application to Glacier Melt Rate Prediction

• Activity Number: 660
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): William Christensen* and Angela Teuscher and Natalie Blades and Aaron Havens and Summer Rupper
• Companies: Brigham Young University and Brigham Young University and Brigham Young University and Brigham Young University and Brigham Young University
• Keywords: regression diagnostics ; outliers ; glacier ; inter-point distances ; extrapolation

Abstract

Regression diagnostics related to influence and leverage have been used for decades to evaluate the extremity of observations found within the space spanned by the predictor variables $X$ = ($X_1$,...,$X_q$). In many applications, the q-dimensional rectangular region formed by the ranges of the predictor variables includes subregions where combinations of the predictors are unlikely or even physically impossible to observe. For potential prediction locations found within such subregions, traditional regression diagnostics may fail to properly quantify the potential risks associated with prediction, particularly when the linear model for the relationship between the response and predictors contains polynomial terms that characterize nonlinear relationships.

In this talk, we consider a broader definition of extrapolation based on the inter-point distances among the points in the training data and we propose graphical and numerical approaches for assessing the potential for extrapolation. Methods are illustrated using data associated with the prediction of glacier melt rates.