The general goodness-of-fit tests for correlated data
The general goodness-of-fit tests for correlated data
复制标题
DOI：
10.1016/j.csda.2021.107379
复制
发表时间：
2022-03
期刊：
影响因子：
--
通讯作者：
Hong Zhang;Zheyang Wu
中科院分区：
文献类型：
--
作者：
Hong Zhang;Zheyang Wu
用拟合优度类型检验分析相关数据是许多应用中的关键统计问题。一个统一的框架，通过一般家庭的拟合优度测试（GGOF），以解决这个问题。GGOF族涵盖了许多经典的和新发展的检验，如最小p值检验、Simes检验、GATES检验、单侧Kolmogorov-Smirnov型检验、单侧φ-散度检验、广义Higher Criticism检验、广义Berk-Jones检验等。GGOF-O仍然包含在GGOF族中，并且在计算上是高效的。为了分析控制GGOF检验的I类错误率，在正等相关的高斯模型下推导了精确的计算方法。在此基础上，提出了有效相关系数（ECC）算法来解决任意相关性问题。模拟是用来探索如何信号和相关模式共同影响典型的GGOF测试的统计功率。GGOF-O在各种信号和相关模式中显示出强大的鲁棒性。正如骨密度研究所证明的，GGOF框架在遗传汇总数据分析中具有检测新疾病基因的良好潜力。CRAN上的R packageSetTest中提供了计算工具。
Analyzing correlated data by goodness-of-fit type tests is a critical statistical problem in many applications. A unified framework is provided through a general family of goodness-of-fit tests (GGOF) to address this problem. The GGOF family covers many classic and newly developed tests, such as the minimalp-value test, Simes test, the GATES, one-sided Kolmogorov-Smirnov type tests, one-sided phi-divergence tests, the generalized Higher Criticism, the generalized Berk-Jones, etc. It is shown that the omnibus test that automatically adapts among GGOF statistics for given data, i.e., the GGOF-O, is still contained in the GGOF family and is computationally efficient. For analytically controlling the type I error rate of any GGOF tests, exact calculation is deduced under the Gaussian model with positive equal correlations. Based on that, the effective correlation coefficient (ECC) algorithm is proposed to address arbitrary correlations. Simulations are used to explore how signal and correlation patterns jointly influence typical GGOF tests' statistical power. The GGOF-O is shown robustly powerful across various signal and correlation patterns. As demonstrated by a study of bone mineral density, the GGOF framework has good potential for detecting novel disease genes in genetic summary data analysis. Computational tools are available in the R packageSetTeston the CRAN.