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Testing a global hypothesis for a set of variables is a fundamental problem in statistics with a wide range of applications. A few well-known classical tests include the Hotelling's T2 test, the F-test, and the empirical Bayes based score test. These classical tests, however, are not robust to the signal strength and could have a substantial loss of power when signals are weak or moderate, a situation we commonly encounter in contemporary applications. In this article, we propose a minimax optimal ridge-type set test (MORST), a simple and generic method for testing a global hypothesis. The power of MORST is robust and considerably higher than that of the classical tests when the strength of signals is weak or moderate. In the meantime, MORST only requires a slight increase in computation compared to these existing tests, making it applicable to the analysis of massive genome-wide data. We also provide the generalizations of MORST that are parallel to the traditional Wald test and Rao's score test in asymptotic settings. Extensive simulations demonstrated the robust power of MORST and that the Type I error of MORST was well controlled. We applied MORST to the analysis of the whole-genome sequencing data from the Atherosclerosis Risk in Communities study, where MORST detected 20%–250% more signal regions than the classical tests. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider in this article detection of signal regions associated with disease outcomes in whole genome association studies. Gene- or region-based methods have become increasingly popular in whole genome association analysis as a complementary approach to traditional individual variant analysis. However, these methods test for the association between an outcome and the genetic variants in a prespecified region, for example, a gene. In view of massive intergenic regions in whole genome sequencing (WGS) studies, we propose a computationally efficient quadratic scan (Q-SCAN) statistic based method to detect the existence and the locations of signal regions by scanning the genome continuously. The proposed method accounts for the correlation (linkage disequilibrium) among genetic variants, and allows for signal regions to have both causal and neutral variants, and the effects of signal variants to be in different directions. We study the asymptotic properties of the proposed Q-SCAN statistics. We derive an empirical threshold that controls for the family-wise error rate, and show that under regularity conditions the proposed method consistently selects the true signal regions. We perform simulation studies to evaluate the finite sample performance of the proposed method. Our simulation results show that the proposed procedure outperforms the existing methods, especially when signal regions have causal variants whose effects are in different directions, or are contaminated with neutral variants. We illustrate Q-SCAN by analyzing the WGS data from the Atherosclerosis Risk in Communities study. for this article are available online. [ABSTRACT FROM AUTHOR]