Incorporating Auxiliary Information for Improved Prediction in High Dimensional Datasets: An Ensemble of Shrinkage Approaches

• Activity Number: 22
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Philip Boonstra*+ and Bhramar Mukherjee and Jeremy Michael George Taylor and Stephen Gruber and Mef Nilbert and Victor Moreno
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan and Copenhagen University Hospital and Catalan Institute of Oncology and University of Barcelona
• Keywords: Brier score ; Conditional predictive ordinate ; Deviance information criterion ; Lynch syndrome ; Relative survival analysis

Abstract

We consider predicting a continuous outcome Y using a length-p covariate X, where p is large, with a sample of moderate size (less than p). W, a noisy surrogate for X, is also available in this sample, and Y and W are measured for a large number of additional observations. We propose various shrinkage approaches where the regression coefficients of Y on X are shrunk towards targets that use information derived from the larger, noisy dataset. We compare the proposed shrinkage approaches with ridge regression of Y on X, which does not use W. We present a unified theoretical framework to view all the estimators as targeted ridge estimators. Finally, we propose a hybrid estimator that is able to balance efficiency and robustness in a data-adaptive way. The methods are evaluated in terms of their mean squared prediction error via analytical and simulation studies. In several plausible scenarios, our proposed shrinkage estimators are able to beat the classical ridge estimator in terms of predictive performance.