An improved empirical Bayes test for positive exponential families

Tachen Liang

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An improved empirical Bayes test for positive exponential families

机译：改进的正指数家庭经验贝叶斯检验

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摘要

We exhibit an empirical Bayes test δ*n for a decision problem using a linear error loss in a class of positive exponential families. This empirical Bayes test δ*n possesses the asymptotic optimality, and its associated regret converges to zero with rate n−1(ln n)6 This rate of convergence improves the previous results in the literature in the sense that a faster rate of convergence is achieved under much weaker conditions. Examples are presented to illustrate the performance of the empirical Bayes test δ*n

机译：对于一类正指数族中的线性误差，我们展示了针对决策问题的经验贝叶斯检验δ* n。该经验贝叶斯检验δ* n具有渐近最优性，并且其相关联的后悔以速率n-1（ln n）6收敛至零。在某种意义上，这种收敛速度改善了文献中的先前结果，因为收敛速度更快。在弱得多的条件下实现。举例说明了经验贝叶斯检验δ* n的性能。

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来源
《Statistica neerlandica》 |2002年第3期|346-361|共16页
作者
Tachen Liang;
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作者单位

Wayne State University Detroit USA;

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原文格式 PDF
正文语种 eng
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关键词
asymptotically optimal rate of convergence; regret;

机译：渐近最优收敛速度;后悔;

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专利

1. On empirical Bayes two-tail tests in a positive exponential family [J] . TACHEN LIANG Journal of nonparametric statistics . 2006,第7a8期

机译：关于正指数家族中的经验贝叶斯二尾检验
2. On an improved empirical Bayes estimator for positive exponential families [J] . TACHEN LIANG Journal of nonparametric statistics . 2005,第7期

机译：关于正指数族的改进的经验贝叶斯估计器
3. On a monotone empirical Bayes test in a positive exponential family [J] . Liang T. Journal of Applied Mathematics and Computing . 2010,第1期

机译：在正指数族中的单调经验贝叶斯检验
4. Optimal rates of empirical Bayes tests for a positive exponential family in the case of negatively associated samples [C] . Chen Jiaqing, Liu Cihua The 2nd International Conference on Information Science and Engineering . 2010

机译：负相关样本下正指数族的经验贝叶斯检验的最佳比率
5. Model adequacy tests for exponential family regression models [D] . Magalla, Champa Hemanthi. 2012

机译：指数族回归模型的模型充分性检验
6. On the geometric modeling approach to empirical null distribution estimation for empirical Bayes modeling of multiple hypothesis testing [O] . Baolin Wu -1

机译：在多假设检测中经验贝叶斯建模的经验空缺分布估计几何建模方法
7. Monotone Empirical Bayes Tests for the Continuous One-Parameter Exponential Family [O] . J. C. van Houwelingen 1976

机译：单调经验贝叶斯对连续的单参数指数家庭进行测试
8. Empirical Bayes Procedures for Selecting Good Populations in Positive Exponential Family [R] . Gupta, S. S. , Li, J. 2001

机译：正指数族中选择优良种群的经验贝叶斯程序

An improved empirical Bayes test for positive exponential families

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