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

Weidong Liu; Qi Man Shao

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

Probability 2009-08-11 v1 Statistics Theory Statistics Theory

Authors: Weidong Liu , Qi Man Shao

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

Keywords

cramér type moderate deviation periodogram studentized periodogram simultaneous tests gene expression time series multiple testing

Cite

@article{arxiv.0908.1145,
  title  = {Cram\'{e}r Type Moderate Deviation for the Maximum of the Periodogram with Application to Simultaneous Tests in Gene Expression Time Series},
  author = {Weidong Liu and Qi Man Shao},
  journal= {arXiv preprint arXiv:0908.1145},
  year   = {2009}
}

Comments

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

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

Abstract

Keywords

Cite

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