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In this chapter, we derive a result which is useful in deriving the risk dominance of shrinkage estimators in Gaussian samples with high-dimensional data. In particular, under a very realistic additional assumption, we revise some recent results in literature. On top of revising such important result, we also provide an alternative proof which corrects the preexisting proof and fills in the gaps left in the derivation of some recent methods in literature.

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On a Class of Shrinkage Estimators of Normal Mean in High-Dimensional Data with Unknown Covariance

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  • 发表日期：

    2026年

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  • Arash A. Foroushani,
  • Sévérien Nkurunziza

摘要

In this chapter, we derive a result which is useful in deriving the risk dominance of shrinkage estimators in Gaussian samples with high-dimensional data. In particular, under a very realistic additional assumption, we revise some recent results in literature. On top of revising such important result, we also provide an alternative proof which corrects the preexisting proof and fills in the gaps left in the derivation of some recent methods in literature.