Marginal Asymptotics for the “large P, Small N” Paradigm: with Applications to Microarray Data

The “large p, small n” paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various statistical models and methodologies using genomic data. In this article, we focus on one-sample and two-sample microarray experiments, where the goal is to identify significantly differentially expressed genes. We establish uniform consistency of certain estimators of marginal distribution functions, sample means and sample medians under the large p small n assumption. We also establish uniform consistency of marginal p-values based on certain asymptotic approximations which permit inference based on false discovery rate techniques. The affects of the normalization process on these results is also investigated. Simulation studies and data analyses are used to assess finite sample performance.