This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs.

中文翻译：

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证明极小极大的高斯序列方法：综述

本文回顾了这些不变估计问题中的极小极大最佳等变估计：位置参数、尺度参数和（Wishart）协方差矩阵。我们简要回顾了最佳等变估计量的发展，即在每种情况下相对于右不变 Haar 测度的广义贝叶斯估计量。然后我们通过基于非截断高斯分布给出最不利的先验序列来证明最佳等变过程的极小化。本文中的结果都是已知的，但与文献中的大多数证明相比，我们通过使用平滑的非截断先验序列，带来了一种新鲜且有些统一的方法。这种方法导致极小极大证明中的一些简化。