Incorporating Auxiliary Information for Improved Prediction in High-Dimensional Data Sets: An Ensemble of Shrinkage Approaches

• Activity Number: 296
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Philip S Boonstra*+ and Bhramar Mukherjee and Jeremy Michael George Taylor
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Cross-validation ; Generalized Ridge ; Mean Squared Prediction Error ; Measurement Error ; Ridge Regression

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: with optimal choice of weights, this estimator will yield smaller prediction error than any of its constituents. The methods are evaluated in terms of their mean squared prediction error via analytical and simulation studies.