不平衡样本量下泊松分布参数的适当贝叶斯极大极小估计

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2020-10-01 DOI:10.1214/19-BJPS459
Y. Hamura, T. Kubokawa
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引用次数: 2

摘要

本文考虑了在加权标准平方误差损失下,可能存在不平衡样本量的独立泊松分布参数的同时估计问题。提出了一类利用样本大小的不平衡性质的非均匀贝叶斯收缩估计。为了提供一个理论证明,我们首先推导了该类估计量是适当贝叶斯因而可容许的充分必要条件,然后得到了与可容许条件相容的极大值的充分条件。通过仿真比较了非均匀收缩估计器和均匀收缩估计器。几种估计方法适用于与标准化死亡率有关的数据。
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Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes
In this paper, we consider the problem of simultaneously estimating parameters of independent Poisson distributions in the presence of possibly unbalanced sample sizes under weighted standardized squared error loss. A class of heterogeneous Bayesian shrinkage estimators that utilize the unbalanced nature of sample sizes is proposed. To provide a theoretical justification, we first derive a necessary and sufficient condition for an estimator in the class to be proper Bayes and hence admissible and then obtain sufficient conditions for minimaxity that are compatible with the admissibility condition. Heterogeneous and homogeneous shrinkage estimators are compared by simulation. Several estimation methods are applied to data relating to the standardized mortality ratio.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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