Discussion of “Confidence Intervals for Nonparametric Empirical Bayes Analysis”
Discussion of “Confidence Intervals for Nonparametric Empirical Bayes Analysis”
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“非参数经验贝叶斯分析的置信区间”的讨论
DOI：
10.1080/01621459.2022.2096039
复制
发表时间：
2022
影响因子：
3.7
通讯作者：
Pensky, Marianna
中科院分区：
文献类型：
--
作者：
Pensky, Marianna
我们想从祝贺作者开始。经验贝叶斯估计是一个非常古老、研究得很好的问题。然而，尽管在大多数实际情况下，人们对置信度的界而不是点估计感兴趣，但在经验贝叶斯环境下的置信度区间的构造却被忽略了。作者给出了几种构造置信度区间的方法，如基于F-局部化的同时置信度区间和对z的特定值的Amari置信度区间。他们给出了置信度区间的一般构造，并研究了它们的长度和覆盖概率。这篇论文的最大成功之一是，它提供了一般形式的条件分布情况下的算法。理论结果以渐近形式表示，因此只有当观测次数趋于无穷大时，才能保证足够的覆盖率。随后，Ignatiadis和Wager分别研究了条件分布P(z|μ)属于二项分布、泊松分布或高斯族的最重要的情况。研究表明，置信度区间的构造及其长度在多大程度上取决于条件分布P(z|μ)以及先验密度的类别G。
We would like to start with congratulating the authors. Empirical Bayes estimation is a very old, well studied problem. However, construction of confidence intervals in empirical Bayes setting has been neglected, in spite of the fact that, in the majority of practical situations, one is interested in confidence bounds rather than point estimators.The authors present several procedures for construction of confidence intervals, such as simultaneous confidence intervals via F-localization and AMARI confidence intervals for specific values of z. They provide general constructions of the confidence intervals and study their lengths and coverage probabilities. One of the great successes of the paper is that it offers algorithms in the case of a conditional distribution of a general form. The theoretical results are stated in asymptotic form, so that adequate coverage is guaranteed only as the number of observations tends to infinity. Subsequently, Ignatiadis and Wager examine separately the most important cases where the conditional distribution P (z| μ) belongs to the binomial, the Poisson or the Gaussian family. This investigation reveals, how much the construction of the confidence intervals and their lengths depend on the conditional distribution P (z| μ) as well as the class of prior densities G.
非参数经验贝叶斯估计的通用方法
影响因子：
1.9
作者：
Pensky Marianna
通讯作者：
Pensky Marianna
具有或不具有稀疏性的反卷积密度线性函数估计的极小极大理论
DOI：
10.1214/16-aos1498
发表时间：
2014
期刊：
arXiv: Statistics Theory
影响因子：
--
作者：
M. Pensky
通讯作者：
M. Pensky
影响因子：
4.5
作者：
Lawrence D. Brown;Tommaso Cai;Anirban DasGupta
通讯作者：
Lawrence D. Brown;Tommaso Cai;Anirban DasGupta