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Journal of Probability and Statistics
Volume 2012, Article ID 913560, 14 pages
http://dx.doi.org/10.1155/2012/913560
Research Article

Robust Semiparametric Optimal Testing Procedure for Multiple Normal Means

1Department of Statistics, Iowa State University, Ames, IA 50011, USA
2Department of Veterinary Diagnostic and Production Animal Medicine, Iowa State University, Ames, IA 50011, USA

Received 27 March 2012; Accepted 10 May 2012

Academic Editor: Yongzhao Shao

Copyright © 2012 Peng Liu and Chong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 multiple testing error. 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 normal assumption of alternative means. However, the assumption of a normal distribution is likely violated in practice. In this paper, 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 simulation study and the analysis of a real microarray data with spike-in probes show that the proposed SPOT procedure performs better when compared to other popularly applied procedures.