Bayes minimax ridge regression estimators.

The problem of estimating of the vector β of the linear regression model y = Aβ + ϵ with ϵ ∼ Np(0, σ2Ip) under quadratic loss function is considered when common variance σ2 is unknown. We first find a class of minimax estimators for this problem which extends a class given by Maruyama and Strawderman (<xref>2005</xref>) 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 (<xref>2005</xref>) 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. [ABSTRACT FROM AUTHOR]