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 $G=\exp (o(n^{1/3}))$.

Some constants in Lemma 4.1 are specified. Other context remains the same