论文标题
贝叶斯收缩方法是根据负多项式样本来解决估计和预测问题不平衡问题的方法
Bayesian Shrinkage Approaches to Unbalanced Problems of Estimation and Prediction on the Basis of Negative Multinomial Samples
论文作者
论文摘要
在本文中，我们处理观察到负多元变量的估计和预测问题，尤其是考虑不平衡的设置。首先，处理标准化平方误差损失下的多个负多项式参数向量的问题，并得出了在适当条件下主导UMVU估计量的新的经验贝叶斯估计器。其次，我们考虑估计在kullback-leibler差异下几个多项式表的关节预测密度，并获得了足够的条件，在该条件下，贝叶斯预测密度相对于分层收缩，在该层次缩小方面占据了贝叶斯预测密度与jeffreys相对于Jeffreys的先前。第三，我们提出的贝叶斯估计量和预测密度可改善模拟的风险。最后，讨论了估计负多项式变量的关节预测密度的问题。
In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors under the standardized squared error loss is treated and a new empirical Bayes estimator which dominates the UMVU estimator under suitable conditions is derived. Second, we consider estimation of the joint predictive density of several multinomial tables under the Kullback-Leibler divergence and obtain a sufficient condition under which the Bayesian predictive density with respect to a hierarchical shrinkage prior dominates the Bayesian predictive density with respect to the Jeffreys prior. Third, our proposed Bayesian estimator and predictive density give risk improvements in simulations. Finally, the problem of estimating the joint predictive density of negative multinomial variables is discussed.
