Journal of Statistical Planning and Inference ( IF 0.8 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.jspi.2021.04.001 Djamila Boukehil , Dominique Fourdrinier , Fatiha Mezoued , William E. Strawderman
We consider estimation of the inverse scatter matrix for a scale mixture of Wishart matrices under various Efron-Morris type losses, for , where is the sample covariance matrix. We improve on the standard estimators , where denotes the Moore–Penrose inverse of and is a positive constant, through an unbiased estimator of the risk difference between the new estimators and . Thus we demonstrate that improvements over the standard estimators under a Wishart distribution can be extended under mixing. We give a unified treatement of the two cases where is invertible () and where is singular.
中文翻译:
Efron-Morris型损失下Wishart矩阵的尺度混合的逆散射矩阵的估计
我们考虑逆散射矩阵的估计 对于在各种Efron-Morris类型损失下的Wishart矩阵的比例混合, 为了 , 在哪里 是样本协方差矩阵。我们改进了标准估算器, 在哪里 表示Moore-Penrose的逆 和 通过对新估算器与新估算器之间的风险差异进行无偏估算器得出一个正常数 。因此,我们证明了在Wishart分布下对标准估计量的改进可以在混合下扩展。我们对这两种情况进行统一处理: 是可逆的()和哪里 是单数。