Cramér-type moderate deviation for the maximum of the periodogram with application to simultaneous tests in gene expression time series

Abstract

In this paper, Cramér-type moderate deviations for the maximum of the periodogram and its studentized version are derived. The results are then applied to a simultaneous testing problem in gene expression time series. It is shown that the level of the simultaneous tests is accurate provided that the number of genes G and the sample size n satisfy G=exp(o(n^1/3)).