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球对称分布下 James–Stein 估计量的推广AI 解读

This paper is primarily concerned with extending the results of Stein to spherically symmetric distributions. Specifically, when $X \sim f(\|X - \theta\|^2)$, we investigate conditions under which estimators of the form $X + ag(X)$ dominate $X$ for loss functions $\|\delta - \theta\|^2$ and loss functions which are concave in $\|\delta - \theta\|^2$. Additionally, if the scale is unknown we investigate estimators of the location parameter of the form $X + aVg(X)$ in two…

凹损失下球对称分布位置参数的极小极大估计AI 解读

For $p \geqslant 4$ and one observation $X$ on a $p$-dimensional spherically symmetric distribution, minimax estimators of $\theta$ whose risks are smaller than the risk of $X$ (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For $n$ observations $X_1, X_2, \cdots, X_n$, we have classes of minimax estimators which are better than the usual procedures, such as the best invariant estimator, $\bar{X}$, or a maximum…