Robust semiparametric optimal testing procedure for multiple normal means
Summary: In high-dimensional gene expression experiments such as microarray and RNA-seq experiments, the number of measured variables is huge while the number of replicates is small. As a consequence, hypothesis testing is challenging because the power of tests can be very low after controlling the multiple testing errors. Optimal testing procedures with high average power while controlling false discovery rate are preferred. Many methods were constructed to achieve high power through borrowing information across genes. Some of these methods can be shown to achieve the optimal average power across genes, but only under a normality assumption of alternative means. However, the assumption of a normal distribution is likely violated in practice. We propose a novel semiparametric optimal testing (SPOT) procedure for high-dimensional data with small sample size. Our procedure is more robust because it does not depend on any parametric assumption for the alternative means. We show that the proposed test achieves the maximum average power asymptotically as the number of tests goes to infinity. Both a simulation study and the analysis of real microarray data with spikes in probes show that the proposed SPOT procedure performs better when compared to other popularly applied procedures.
scientific article; zbMATH DE number 6092423