PERMUTATION p-VALUE APPROXIMATION VIA GENERALIZED STOLARSKY INVARIANCE

• 成果类型: Article
• 署名作者: He, Hera Y.; Basu, Kinjal; Zhao, Qingyuan; Owen, Art B.
• 署名单位: Stanford University; University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1702
• 发表日期: 2019
• 页码: 583-611
• 关键词: expression; pathways

摘要

It is common for genomic data analysis to use p-values from a large number of permutation tests. The multiplicity of tests may require very tiny p-values in order to reject any null hypotheses and the common practice of using randomly sampled permutations then becomes very expensive. We propose an inexpensive approximation to p-values for two sample linear test statistics, derived from Stolarsky's invariance principle. The method creates a geometrically derived reference set of approximate p-values for each hypothesis. The average of that set is used as a point estimate (p) over cap and our generalization of the invariance principle allows us to compute the variance of the p-values in that set. We find that in cases where the point estimate is small, the variance is a modest multiple of the square of that point estimate, yielding a relative error property similar to that of saddlepoint approximations. On a Parkinson's disease data set, the new approximation is faster and more accurate than the saddlepoint approximation. We also obtain a simple probabilistic explanation of Stolarsky's invariance principle.