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Hypothesis testing of matrix graph model with application to brain connectivity analysis
Author(s) -
Xia Yin,
Li Lexin
Publication year - 2017
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12633
Subject(s) - computer science , statistical hypothesis testing , oracle , false discovery rate , multiple comparisons problem , matrix (chemical analysis) , power graph analysis , graph , artificial intelligence , data mining , algorithm , pattern recognition (psychology) , theoretical computer science , mathematics , statistics , biochemistry , chemistry , materials science , software engineering , composite material , gene
Summary Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependence that is often encoded in terms of partial correlation. Such a graph is inferred from the matrix‐valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions does not offer a direct statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial‐temporal dependence structure, we develop oracle and data‐driven procedures to test both the global hypothesis that all spatial locations are conditionally independent, and simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control. Our theoretical results show that the data‐driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite‐sample performance of the proposed tests is studied via intensive simulations, and the new tests are applied on a real electroencephalography data analysis.