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Title: Two stage rule to control two-dimensional false discovery rate for composite null hypothesis Authors:  Youngrae Kim - Seoul National University (Korea, South) [presenting]
Johan Lim - Seoul National University (Korea, South)
Jaesik Jeong - Chonnam National University (Korea, South)
Jong Soo Lee - University of Massachusetts Lowell (United States)
Abstract: The mass spectral data are featured as being high dimensional with small number of signals (peaks) and many noisy observations. This unique features of mass spectral data motivates the problem testing of many composite null hypotheses simultaneously. The composite null we consider is the union of two simple hypotheses (e.g., the alternative hypothesis is means of two populations are not same and the variance is not too small so that the observations are from signal). We develop two stage procedure to control the false discovery rate of the simultaneous multiple hypothesis testing. The new procedure provides an explicit boundary in two dimensional space of bivariate test statistics, compared to the existing local false discovery rate (fdr) based procedure. We numerically compare the performance of our procedure to the existing, two-dimensional local false discovery rate (2d-fdr) under various setting, and apply the procedure to differentiating origins of herbal medicine using gas chromatography-mass spectrometry (GC-MS). Finally, we additionally discuss two stage additive procedure for testing many intersection null hypotheses simultaneously.