Cram\'{e}r Type Moderate Deviation for the Maximum of the Periodogram with Application to Simultaneous Tests in Gene Expression Time Series

TL;DR

This paper derives Cramér type moderate deviation results for the maximum of the periodogram and applies these findings to improve simultaneous testing accuracy in gene expression time series analysis.

Contribution

It introduces new Cramér type moderate deviation results for periodogram maxima and demonstrates their application in controlling error rates in gene expression testing.

Findings

Accurate level control for tests when G=exp(o(n^{1/3}))

Derived Cramér type moderate deviations for periodogram maxima

Applied results to gene expression data analysis

Abstract

In this paper, Cram\'{e}r 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 $G=\exp(o(n^{1/3}))$.