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    Intrinsic Data Depth for Hermitian Positive Definite Matrices

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    Type
    Dataset
    Authors
    Chau, Joris
    Ombao, Hernando cc
    von Sachs, Rainer
    KAUST Department
    Biostatistics Group
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2019
    Permanent link to this record
    http://hdl.handle.net/10754/664622
    
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    Abstract
    Nondegenerate covariance, correlation, and spectral density matrices are necessarily symmetric or Hermitian and positive definite. This article develops statistical data depths for collections of Hermitian positive definite matrices by exploiting the geometric structure of the space as a Riemannian manifold. The depth functions allow one to naturally characterize most central or outlying matrices, but also provide a practical framework for inference in the context of samples of positive definite matrices. First, the desired properties of an intrinsic data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two pointwise and integrated data depth functions that satisfy each of these requirements and investigate several robustness and efficiency aspects. As an application, we construct depth-based confidence regions for the intrinsic mean of a sample of positive definite matrices, which is applied to the exploratory analysis of a collection of covariance matrices in a multicenter clinical trial. Supplementary materials and an accompanying R-package are available online.
    Citation
    Chau, J., Ombao, H., & Sachs, R. V. (2019). Intrinsic Data Depth for Hermitian Positive Definite Matrices [Data set]. Taylor & Francis. https://doi.org/10.6084/M9.FIGSHARE.7393223.V3
    Publisher
    Taylor & Francis
    DOI
    10.6084/m9.figshare.7393223.v3
    Relations
    Is Supplement To:
    • [Article]
      Chau J, Ombao H, von Sachs R (2018) Intrinsic Data Depth for Hermitian Positive Definite Matrices. Journal of Computational and Graphical Statistics: 1–25. Available: http://dx.doi.org/10.1080/10618600.2018.1537926.. DOI: 10.1080/10618600.2018.1537926 HANDLE: 10754/631388
    ae974a485f413a2113503eed53cd6c53
    10.6084/m9.figshare.7393223.v3
    Scopus Count
    Collections
    Datasets; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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