Comparisons of the Stein-type and Nonparametric Shrinkage Predictions

• Activity Number: 233
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Xue Xin*+ and Leann Myers
• Companies: Tulane University and Tulane University
• Keywords: shrinkage ; prediction ; MSEP ; PRESS

Abstract

Different forms of shrinkage correction have been proposed by researchers when the regression model is used for prediction. The Stein-type and nonparametric shrinkage predictors were compared using resampling and sample-reusing techniques. P (number of predictors), n (sample size), beta, and the correlation structure of the VC matrices were varied. Both the mean and median of the mean squared error for prediction (MSEP) and PRESS were generated from 10,000 simulations (5,000 for PRESS) and the results were compared. Shrinkage predictions gave a uniformly lower MSEP/PRESS than the least squares predictions. The percentage of loss saving went up to 35% under certain conditions. Furthermore, the Stein-type usually gave a lower MSEP/ PRESS than the nonparametric form. The percentage of loss saving decreased as the sample size increased or the number of covariates decreased. The percentages of loss saving were fairly comparable when the covariates were either independent or had low (pairwise r = 0.1) to moderate (pairwise r = 0.4) correlation. The findings were the same whether means or medians of MSEP and PRESS were considered.