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Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data

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  • Dong, Kai
  • Pang, Herbert
  • Tong, Tiejun
  • Genton, Marc G.

Abstract

High-throughput expression profiling techniques bring novel tools and also statistical challenges to genetic research. In addition to detecting differentially expressed genes, testing the significance of gene sets or pathway analysis has been recognized as an equally important problem. Owing to the “large p small n” paradigm, the traditional Hotelling’s T2 test suffers from the singularity problem and therefore is not valid in this setting. In this paper, we propose a shrinkage-based diagonal Hotelling’s test for both one-sample and two-sample cases. We also suggest several different ways to derive the approximate null distribution under different scenarios of p and n for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when n is moderate or large, but it is better when n is small. In addition, we analyze four gene expression data sets and they demonstrate the advantage of our proposed shrinkage-based diagonal Hotelling’s test.

Suggested Citation

  • Dong, Kai & Pang, Herbert & Tong, Tiejun & Genton, Marc G., 2016. "Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 127-142.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:127-142
    DOI: 10.1016/j.jmva.2015.08.022
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    References listed on IDEAS

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    2. Ouyang, Yanyan & Liu, Jiamin & Tong, Tiejun & Xu, Wangli, 2022. "A rank-based high-dimensional test for equality of mean vectors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Xiao Min & Chen Ting & Huang Kunpeng & Ming Ruixing, 2020. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing," Journal of Systems Science and Information, De Gruyter, vol. 8(6), pages 549-564, December.
    4. Issouani, El Mehdi & Bertail, Patrice & Gautherat, Emmanuelle, 2024. "Exponential bounds for regularized Hotelling’s T2 statistic in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    5. Jin-Ting Zhang & Bu Zhou & Jia Guo, 2022. "Testing high-dimensional mean vector with applications," Statistical Papers, Springer, vol. 63(4), pages 1105-1137, August.

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