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    A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors

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    Type
    Preprint
    Authors
    Hu, Zongliang
    Tong, Tiejun
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Spatio-Temporal Statistics and Data Analysis Group
    Statistics Program
    Date
    2020-03-10
    Permanent link to this record
    http://hdl.handle.net/10754/662286
    
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    Abstract
    For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, we propose a pairwise Hotelling method for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, we construct the new test statistics as the summation of Hotelling's test statistics for the covariate pairs with strong correlations and the squared $t$ statistics for the individual covariates that have little correlation with others. We further derive the asymptotic null distributions and power functions for the proposed Hotelling tests under some regularity conditions. Numerical results show that our new tests are able to control the type I error rates, and can achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed and they both demonstrate the efficacy of our pairwise Hotelling tests.
    Publisher
    arXiv
    arXiv
    2003.04636
    Additional Links
    https://arxiv.org/pdf/2003.04636
    Collections
    Preprints; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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