Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location
Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location
复制标题
具有参数约束的贝叶斯预测密度估计，用于未知位置的指数分布
DOI：
10.1007/s00184-021-00840-3
复制
发表时间：
2022
期刊：
影响因子：
0.7
通讯作者：
Kubokawa Tatsuya
中科院分区：
文献类型：
--
作者：
Hamura Yasuyuki;Kubokawa Tatsuya
本文考虑位置未知的指数分布的预测问题。在大多数情况下，我们处理一维的情况，并假设位置参数被限制在一个区间内。在Kullback-Leibler散度下，比较了实线和受限空间上关于先验密度的贝叶斯预测密度。我们首先考虑标度参数已知的情况。我们得到了一般的占优条件以及极小公理和可容许性结果。接下来，我们来处理规模未知的情况。在这种情况下，假设位置参数小于已知常数，并得到了控制的充分条件。最后，我们处理了一个已知规模的多维问题，其中位置参数被限制在一个凸集上。通过仿真研究了几种贝叶斯预测密度的性能。其中一些预测方法被应用于实际数据。
In this paper, we consider prediction for the exponential distribution with unknown location. For the most part, we treat the one-dimensional case and assume that the location parameter is restricted to an interval. The Bayesian predictive densities with respect to prior densities supported on the real line and the restricted space are compared under the Kullback–Leibler divergence. We first consider the case where the scale parameter is known. We obtain general dominance conditions and also minimaxity and admissibility results. Next, we treat the case of unknown scale. In this case, the location parameter is assumed to be less than a known constant and sufficient conditions for domination are obtained. Finally, we treat a multidimensional problem with known scale where the location parameter is restricted to a convex set. The performance of several Bayesian predictive densities is investigated through simulation. Some of the prediction methods are applied to real data.