论文标题
贝叶斯的收缩量估计负多项式参数向量
Bayesian Shrinkage Estimation of Negative Multinomial Parameter Vectors
论文作者
论文摘要
负多项式分布是负二项式分布的多元概括。在本文中，我们考虑了根据标准化平方误差损失下的负多项式变量的观察，估算概率矩阵的问题。首先，得出了收缩估计器主导UMVU估计器的一般条件，并构建了满足条件的经验贝叶斯估计量。接下来，引入了层次收缩率，在某些条件下显示了相关的贝叶斯估计量在UMVU估计器中占主导地位，并提供了有关后验计算的一些评论。最后，通过模拟比较收缩估计器和UMVU估计器。
The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative multinomial variables under the standardized squared error loss. First, a general sufficient condition for a shrinkage estimator to dominate the UMVU estimator is derived and an empirical Bayes estimator satisfying the condition is constructed. Next, a hierarchical shrinkage prior is introduced, an associated Bayes estimator is shown to dominate the UMVU estimator under some conditions, and some remarks about posterior computation are presented. Finally, shrinkage estimators and the UMVU estimator are compared by simulation.
