Maximum pairwise Bayes factors for covariance structure testing
Maximum pairwise Bayes factors for covariance structure testing
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DOI：
10.1214/21-ejs1900
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发表时间：
2018-09
影响因子：
1.1
通讯作者：
Kyoungjae Lee;Lizhen Lin;D. Dunson
中科院分区：
文献类型：
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作者：
Kyoungjae Lee;Lizhen Lin;D. Dunson
协方差矩阵结构的假设检验非常重要，但在高维环境中面临着巨大的挑战。尽管一致的频率主义单样本协方差检验已经被提出，但对于大型协方差矩阵，缺乏简单的、计算上可扩展的、理论上合理的贝叶斯检验方法。出于这一差距以及对针对稀疏替代方案的强大测试的需求，我们提出了一种基于最大成对贝叶斯因子的新颖测试框架。我们最初的重点是单样本协方差检验；所提出的检验可以在频率渐近意义上最佳地区分无效假设和替代假设。然后，我们提出对角线测试和可扩展的协方差图选择程序，这些程序被证明是一致的。模拟研究评估了相对于竞争对手所提出的方法。我们的图形选择方法的性能通过声纳数据集的应用得到了证明。
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of simple, computationally scalable, and theoretically sound Bayesian testing methods for large covariance matrices. Motivated by this gap and by the need for tests that are powerful against sparse alternatives, we propose a novel testing framework based on the maximum pairwise Bayes factor. Our initial focus is on one-sample covariance testing; the proposed test can optimally distinguish null and alternative hypotheses in a frequentist asymptotic sense. We then propose diagonal tests and a scalable covariance graph selection procedure that are shown to be consistent. A simulation study evaluates the proposed approach relative to competitors. The performance of our graph selection method is demonstrated through applications to a sonar data set.