Bayes minimax ridge regression estimators

S. Zinodiny

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 22, 5519-5533

Abstract: 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 (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.

Date: 2018
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DOI: 10.1080/03610926.2017.1397167

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