Statistical tests for large tree-structured data

Bharath, Karthik, Kambadur, Prabhanjan, Dey, Dipak. K., Rao, Arvind and Baladandayuthapani, Veerabhadran (2017) Statistical tests for large tree-structured data. Journal of the American Statistical Association, 112 (520). pp. 1733-1743. ISSN 1537-274X

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We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from which we develop a class of invariant tests. Using the model for binary trees, we then construct tests for general trees by using the distributional properties of the Continuum Random Tree, which arises as the invariant limit for a broad class of models for tree-structured data based on conditioned Galton–Watson processes. The test statistics for the goodness-of-fit tests are simple to compute and are asymptotically distributed as χ2 and F random variables. We illustrate our methods on an important application of detecting tumour heterogeneity in brain cancer. We use a novel approach with tree-based representations of magnetic resonance images and employ the developed tests to ascertain tumor heterogeneity between two groups of patients.

Item Type: Article
Additional Information: The Version of Record of this manuscript has been published and is available in Journal of the American Statistical Association 07 Aug 2017
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number:
Depositing User: Bharath, Karthik
Date Deposited: 24 Feb 2017 08:38
Last Modified: 04 May 2020 18:59

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