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多元分布的最优Fisher信息AI 解读

It is shown that within the class of all multivariate distributions depending on a location parameter (and satisfying certain smoothness conditions) and with a weighted norm constraint on the covariance matrix, the one with minimum Fisherian information is the Gaussian distribution. This result is then used in obtaining a tight upper bound on the error of estimating an unknown random vector observed in additive Gaussian noise under quadratic loss.

广义二次损失下正态随机向量均值的极小极大估计AI 解读

An admissible minimax estimate for the mean of a normal random vector with known covariance is derived for a generalized quadratic loss function. This loss function is quadratic in both the estimation error and the unknown mean. The estimate is derived using the method of least favorable prior distributions. The decision rule is linear, and the least favorable prior distribution for the unknown mean is normal with zero mean. The covariance of this least favorable normal…