Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation methods which shrink an unstructured, group-specific covariance either across groups towards a pooled covariance or within each group towards a Kronecker structure have been developed. However, in many applications, it is unclear which approach will result in more accurate covariance estimates. In this article, we present a hierarchical prior distribution which flexibly allows for both types of shrinkage. The prior linearly combines shrinkage across groups towards a shared pooled covariance and shrinkage within groups towards a group-specific Kronecker covariance. We illustrate the utility of the proposed prior in speech recognition and an analysis of chemical exposure data.

翻译：多组矩阵变量数据在组内样本量较小的情况下进行协方差估计，是现代应用中许多数据分析任务的关键组成部分。为获得精确的组特异性协方差估计，已有研究开发了收缩估计方法，这些方法将非结构化的组特异性协方差跨组向合并协方差收缩，或在组内向克罗内克结构收缩。然而，在许多应用中，尚不清楚哪种方法能产生更精确的协方差估计。本文提出了一种分层先验分布，该分布灵活地允许两种类型的收缩。该先验线性地结合了跨组向共享合并协方差的收缩以及组内向组特异性克罗内克协方差的收缩。我们通过语音识别和化学暴露数据分析展示了所提出先验的实用性。