Statistical Tests for Large Tree-Structured Data

• 成果类型: Article
• 署名作者: Bharath, Karthik; Kambadur, Prabhanjan; Dey, Dipak K.; Rao, Arvind; Baladandayuthapani, Veerabhadran
• 署名单位: University of Nottingham; Bloomberg L.P.; University of Connecticut; University of Texas System; UTMD Anderson Cancer Center; University of Texas System; UTMD Anderson Cancer Center
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1240081
• 发表日期: 2017
• 页码: 1733-1743
• 关键词: graphs

摘要

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 chi(2) and F random variables. We illustrate our methods on an important application of detecting tumor heterogeneity in brain cancer. We use a novel approach with treebased representations of magnetic resonance images and employ the developed tests to ascertain tumor heterogeneity between two groups of patients. Supplementary materials for this article are available online.