Type
DatasetKAUST Department
Biostatistics GroupComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program
Date
2019Permanent link to this record
http://hdl.handle.net/10754/664622
Metadata
Show full item recordAbstract
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.V3Publisher
Taylor & FrancisRelations
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