In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.

翻译：在这项工作中,调查了不同类别收缩估计值的多变正常平均值的估计。 与平衡损失函数相关的风险被用于比较两个估计值。 我们首先考虑对詹姆斯- 斯泰因估计值进行概括的估算值, 并显示这些估计值在最大概率估计值( MLE) 中占主导地位, 因此当收缩功能满足某些条件时, 它们是微缩的。 然后, 我们对待多等式的估算值, 并证明多等式的测量值的提高, 使得我们能从先前构建的测量值中 建立一个更好的估计值 。