This paper proposes a new generalized extended balanced loss function (GEBLF). Admissibility of linear estimators is characterized in the General Gauss–Markov model with respect to GEBLF. The sufficient and necessary conditions for linear estimators to be admissible with a dispersion matrix possibly singular among the set of linear estimators are obtained. It is stated that the results obtained under special conditions lead to the results known in the literature.

中文翻译：

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广义扩展平衡损失函数下一般 Gauss-Markov 模型中的容许线性估计量

本文提出了一种新的广义扩展平衡损失函数（GEBLF）。线性估计量的可接受性在关于 GEBLF 的通用高斯-马尔可夫模型中表征。得到了线性估计量在线性估计量集合中具有可能奇异的色散矩阵的充分必要条件。据说在特殊条件下获得的结果导致了文献中已知的结果。