  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.
