Abstract:
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Beta mixture models are used to describe a large collection of p-values from numerous hypothesis tests, in which case one of the mixture components may be taken to be a uniform distribution (Allison et al, 2002). Dai and Charnigo (2008) referred to such a two-component mixture as a beta contamination model and provided methods for testing whether the two-component beta contamination model could be reduced to a uniform distribution. However, an empirical distribution of p-values may be more complicated than what can be described with a two-component beta contamination model. In this work, we consider a three-component beta contamination model with a parameter space which is limited to guarantee identifiability. We explore how to test a null hypothesis that a three-component model can be reduced to two components. We define a test statistic and perform simulations to identify its critical value. As a case study, we apply this test statistic to a real microarray dataset.
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