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球对称误差下线性模型系数的改进置信集AI 解读

Under the assumption of normal errors, confidence spheres for $p(p \geq 3)$ coefficients of a linear model centered at the positive part James-Stein estimators were recently proved, by Hwang and Casella, to dominate the usual confidence set with the same radius. In this paper, the same domination results are established under various spherically symmetric distributions. These distributions include uniform distributions, double exponential distributions, and multivariate $t$ d…

普遍支配与随机支配：广泛损失函数下的同时估计比较AI 解读

In Wald's statistical decision theory, the criterion of domination (or uniform betterness) is defined with respect to a specific loss. In practice, however, the exact form of a loss function is difficult to specify. Hence, it is important to study the domination criterion simultaneously under a class of loss functions. In this paper we focus on estimation problems. We mainly investigate the possibility of domination simultaneously under the class of loss functions $L(|\theta - \delta|)$…

Stein估计的数据平滑性质AI 解读

The data smoothing aspect of Stein estimates is explored in the nonparametric regression settings. We show that appropriately shrinking the raw data towards any linear smoother will provide a robust "smoother" (which dominates the raw data and hence has a bounded maximum risk when the average squared error loss is concerned).

多元正态分布均值的经验贝叶斯置信集AI 解读

Through the use of an empirical Bayes argument, a confidence set for the mean of a multivariate normal distribution is derived. The set is a recentered sphere, is easy to compute, and has uniformly smaller volume than the usual confidence set. An exact formula for the coverage probability is derived, and numerical evidence is presented which shows that the empirical Bayes set uniformly dominates the usual set in coverage probability.

离散指数族多参数估计中改进估计量的构造AI 解读

This paper extends and unifies the theory of simultaneous estimation for the discrete exponential family. We discuss construction of estimators which theoretically dominate the uniformly minimum variance unbiased estimator (UMVUE) under a weighted squared error loss function, and show by means of computer simulation results that new simultaneous Poisson means estimators perform more favorably than those previously proposed. Our improved estimators shift the UMVUE towards a…

离散指数族可容许估计量的半尾部上界及其应用AI 解读

Admissibility problems involving simultaneous estimation in discrete exponential families are studied by solving difference inequalities. It is shown that if an estimator is admissible under the loss function $L_m(\mathbf{\theta, a)} = \sum^p_{i = 1} \theta^{m_i}_i (\theta_i - a_i)^2$, then in the tail (i.e., for large values of the observations), this estimator has to be less than certain bounds. Specific bounds, called Semi Tail Upper Bounds (STUB), are given here. These…

多元正态均值的极小极大置信集AI 解读

For the problem of estimating a $p$-variate normal mean, the existence of confidence procedures which dominate the usual one, a sphere centered at the observations, has long been known. However, no explicit procedure has yet been shown to dominate. For $p \geq 4$, we prove that if the usual confidence sphere is recentered at the positive-part James Stein estimator, then the resulting confidence set has uniformly higher coverage probability, and hence is a minimax confidence…

离散指数族中标准估计量的改进：泊松与负二项情形AI 解读

Assume that $X_1, \cdots, X_p$ are independent random observations having discrete exponential densities $\rho_i(\theta_i)t_i(x_i)\theta^{xi}_i, i = 1, \cdots, p$ respectively. A general technique of improving upon the uniform minimum variance unbiased estimator (UMVUE) of $(\theta_1, \cdots, \theta_p)$ is developed under possibly weighted squared error loss functions. It is shown that improved estimators can be constructed by solving a difference inequality. Typical…