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Bayes minimax ridge regression estimators

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  • S. Zinodiny

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.

Suggested Citation

  • S. Zinodiny, 2018. "Bayes minimax ridge regression estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5519-5533, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:22:p:5519-5533
    DOI: 10.1080/03610926.2017.1397167
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