High-dimensional test for one-sided hypotheses

Advances in data acquisition technologies and computational resources have significantly improved the analysis of large datasets across various domains. These datasets often feature a high number of variables but a limited number of observations, commonly referred to as "high-dimensional data." Analyzing such data requires innovative statistical methods to further scientific insights. Mean vector testing plays a vital role in many scientific investigations. Although considerable research has been devoted to developing efficient methods for two-sided mean vector tests in high-dimensional data-such as those used to identify differentially expressed genes-one-sided high-dimensional mean vector tests have not been as thoroughly explored. These tests are particularly valuable for detecting significantly up-regulated or down-regulated gene sets within predefined groups. Addressing this need, we introduce a new method: the Sum Max-Component (SMC) test. We have explored the asymptotic behavior of the SMC test statistic as both the sample size and the data dimensions grow indefinitely. SMC test method has undergone extensive validation in finite sample scenarios, where it has proven to be effective, showing competitive rates for both type I error and power. To illustrate its practical applications, we have employed the SMC test in a gene set enrichment analysis on the proteomic data of ovarian cancer patients from the National Cancer Institute's CPTAC study, underscoring its potential value in ovarian cancer biology. Multivariate one-sided test, High-dimensional data, Gaussian-type tails, Exponential-type tails, enrichment analysis, high-grade serous ovarian cancer.