Motivation: A primary objective of microarray studies is to determine genes which are differentially expressed under various conditions. Parametric tests, such as two-sample t-tests, may be used to identify differentially expressed genes, but they require some assumptions that are not realistic for many practical problems. Non-parametric tests, such as empirical Bayes methods and mixture normal approaches, have been proposed, but the inferences are complicated and the tests may not have as much power as parametric models.
Results: We propose a weakly parametric method to model the distributions of summary statistics that are used to detect differentially expressed genes. Standard maximum likelihood methods can be employed to make inferences. For illustration purposes the proposed method is applied to the leukemia data (training part) discussed elsewhere. A simulation study is conducted to evaluate the performance of the proposed method.