A sharp boundary for SURE-based admissibility for the normal means problem under unknown scale

作者：Maruyama Yuzo^*; Strawderman William E

来源：Journal of Multivariate Analysis, 2017, 162: 134-151.

DOI：10.1016/j.jmva.2017.09.002

• Admissibility
• Stein's unbiased risk estimate
• Generalized Bayes

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined in terms of nonexistence/existence of a solution to a differential inequality based on Stein's unbiased risk estimate (SURE). We find a sharp boundary between quasi-admissible and quasi inadmissible estimators related to the optimal James Stein estimator. We also find a class of priors related to the Strawderman class in the known variance case where the boundary between quasi-admissibility and quasi-inadmissibility corresponds to the boundary between admissibility and inadmissibility in the known variance case. Additionally, we also briefly consider generalization to the case of general spherically symmetric distributions with a residual vector.

• 出版日期2017-11
• 单位rutgers