Bayes minimax ridge regression estimators

The problem of estimating of the vector of the linear regression model y = A + E with E approximate to N-p(0, sigma I-2(p)) under quadratic loss function is considered when common variance sigma(2) is unknown. We first find a class of minimax estimators for this problem which extends a class given by Maruyama and Strawderman (2005) and using these estimators, we obtain a large class of (proper and generalized) Bayes minimax estimators and show that the result of Maruyama and Strawderman (2005) is a special case of our result. We also show that under certain conditions, these generalized Bayes minimax estimators have greater numerical stability (i.e., smaller condition number) than the least-squares estimator.