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贝叶斯极小极大估计量的构造AI 解读

Bayes estimation of the mean of a multivariate normal distribution is considered under quadratic loss. We show that, when particular spherical priors are used, the superharmonicity of the square root of the marginal density provides a viable method for constructing (possibly proper) Bayes (and admissible) minimax estimators. Examples illustrate the theory; most notably it is shown that a multivariate Student-$t$ prior yields a proper Bayes minimax estimate.

一般线性模型中球对称分布下的损失估计AI 解读

This paper is concerned with estimating the loss of a point estimator when sampling from a spherically symmetric distribution. We examine the canonical setting of a general linear model where the dimension of the parameter space is greater than 4 and less than the dimension of the sampling space. We consider two location estimators--the least squares estimator and a shrinkage estimator--and we compare their unbiased loss estimator with an improved loss estimator. The…