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二次损失下位置参数的同时估计AI 解读

Simultaneous estimation of $p(p \geq 3)$ location parameters are considered under quadratic loss. Explicit estimators which dominate the best invariant one are given mainly when coordinates of the best invariant one are independently, identically and symmetrically distributed. Effectiveness of integration by parts in evaluating the risk function of the dominating estimator is shown for three typical continuous distributions (uniform, double exponential and $t$). Further…

一类二次损失函数下的多元正态均值估计AI 解读

Stein's estimator for p ≧ 3 normal means is known to dominate the usual estimator if the loss is quadratic. Brown (1975) has shown that for a class of quadratic loss functions the usual estimator can be uniformly improved if the loss functions do not give such extreme weights to the coordinates that the problem essentially reduces to a two-dimensional one. However, he has not given a uniformly better estimator. In this article, we give explicit alternatives that uniformly…

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参数同时估计中单个估计量的精度AI 解读

Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are…