3995

Journal of Computational and Graphical Statistics

American Statistical Association

1998

7

3

397-416

Bayesian prior , Bridge regressions , GCV , Newton–Raphson , Shrinkage , Shooting method

Bridge regression, a special family of penalized regressions of a penalty function jj j with 1, is considered. A general approach to solve for the bridge estimator is developed. A new algorithm for the lasso ( = 1) is obtained by studying the structure of the bridge estimators. The shrinkage parameter and the tuning parameter are selected via generalized cross-validation (GCV). Comparison between the bridge model ( 1) and several other shrinkage models, namely the ordinary least squares regression ( = 0), the lasso ( = 1) and ridge regression ( = 2), is made through a simulation study. It is shown that the bridge regression performs well compared to the lasso and ridge regression. These methods are demonstrated through an analysis of a prostate cancer data. Some computational advantages and limitations are discussed.