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

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    Type
    Article
    Authors
    Dong, Kai
    Pang, Herbert
    Tong, Tiejun
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2015-09-16
    Online Publication Date
    2015-09-16
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/578818
    
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    Abstract
    DNA sequencing 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 pp small nn” paradigm, the traditional Hotelling’s T2T2 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 pp and nn for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when nn is moderate or large, but it is better when nn 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.
    Citation
    Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data 2015 Journal of Multivariate Analysis
    Publisher
    Elsevier BV
    Journal
    Journal of Multivariate Analysis
    DOI
    10.1016/j.jmva.2015.08.022
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S0047259X15002146
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jmva.2015.08.022
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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