Performance of Shrinkage Estimators for Prediction in Multiple Regression--Future X-Random Prediction Error

• Activity Number: 219
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 9:00 AM to 10:50 AM
• Sponsor: ENAR
• Author(s): Xue Xin*+ and Leann Myers
• Companies: Tulane University and Tulane University
• Keywords: multiple regression ; shrinkage ; prediction ; MSEP

Abstract

Regression models in medical research are widely used for predictions. When predicting the response at a future randomly chosen covariate vector x, problems can arise. The fit of a regression model to new data is nearly always worse than its fit to the original data, a deterioration known as shrinkage. The Stein-type predictors give a uniformly lower mean squared error for prediction (MSEP) than least squares estimators under certain assumptions. Three different forms of the Stein-type shrinkage prediction were computed and compared using resampling and cross-validation. In addition, a nonparametric estimator proposed by Copas was computed to estimate shrinkage directly. Data were generated from models with normally and non-normally distributed error terms. Normal cases for residual variances following particular patterns of heteroscedasticity were investigated. Non-normally distributed error terms from both symmetric and asymmetric distributions were examined. The parameters p (number of predictors), n, beta and the correlation structure of the design matrices were varied. Suggestions for applied usage of shrinkage prediction using multiple regression were proposed.