We consider a linear regression model with a vector of bounded parameters and a centered noise vector that has an uncertain unimodal distribution but known covariance matrix. We pose the minimax estimation problem for a linear combination of unknown parameters with the use of the probability criterion. The minimax estimate is determined as a result of minimizing a probability bound over the region of possible values of the variance and squared bias for all possible linear estimates. We establish that the resulting robust solution is less conservative in comparison with wider classes of distributions.

中文翻译：

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单峰噪声和有界参数下具有概率准则的Minimax线性估计。

我们考虑一个线性回归模型，该模型具有有限参数向量和中心噪声向量，该向量具有不确定的单峰分布但已知协方差矩阵。我们使用概率准则对未知参数的线性组合提出最小极大估计问题。确定最小极大值估计是将所有可能的线性估计的方差和平方偏差的可能值区域上的概率最小化的结果。我们确定，与更广泛的分布类别相比，所得的健壮解决方案不那么保守。