A statistical shrinkage model and its applications

Bridge regression, a special type of penalized regression of a penalty function with is considered. The Bridge estimator is obtained by solving the penalized score equations via the modified Newton-Raphson method or the Shooting method. The Bridge estimator yields small variance with a little sacrifice of bias. And thus achieves small mean squared error and small prediction error when collinearity is present among regressors in a linear regression model.The concept of penalization is generalized via the penalized score equations, which allow the implementation of penalization regardless of the existence of joint likelihood functions. Penalization is then applied to generalized linear models and generalized estimating equations (GEE).The penalty parameter and the tuning parameter are selected via the generalized cross-validation (GCV). A quasi-GCV is developed to select the parameters for the penalized GEE.