Statistical tests for large tree-structured data

Bharath, Karthik; Kambadur, Prabhanjan; Dey, Dipak. K.; Rao, Arvind; Baladandayuthapani, Veerabhadran

Abstract

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.

Citation

Bharath, K., Kambadur, P., Dey, D. K., Rao, A., & Baladandayuthapani, V. (in press). Statistical tests for large tree-structured data. Journal of the American Statistical Association, 112(520), https://doi.org/10.1080/01621459.2016.1240081

• Journal Article Type: Article
• Acceptance Date: Sep 8, 2016
• Online Publication Date: Aug 7, 2017
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Aug 8, 2018
• Journal: Journal of the American Statistical Association
• Print ISSN: 0162-1459
• Electronic ISSN: 1537-274X
• Publisher: Taylor & Francis Open
• Peer Reviewed: Peer Reviewed
• Volume: 112
• Issue: 520
• DOI: https://doi.org/10.1080/01621459.2016.1240081
• Public URL: https://nottingham-repository.worktribe.com/output/876891
• Publisher URL: http://www.tandfonline.com/doi/full/10.1080/01621459.2016.1240081
• 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 http://www.tandfonline.com/10.1080/01621459.2016.1240081