Nonparametric independence tests in high-dimensional settings, with applications to the genetics of complex disease

• URL: http://arxiv.org/abs/2407.19624v1
• Date: Mon, 29 Jul 2024 01:00:53 GMT
• Title: Nonparametric independence tests in high-dimensional settings, with applications to the genetics of complex disease
• Authors: Fernando Castro-Prado,
• Abstract summary: We show how defining adequate premetric structures on the support spaces of the genetic data allows for novel approaches to such testing. For each problem, we provide mathematical results, simulations and the application to real data.
• Score: 55.2480439325792
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: [PhD thesis of FCP.] Nowadays, genetics studies large amounts of very diverse variables. Mathematical statistics has evolved in parallel to its applications, with much recent interest high-dimensional settings. In the genetics of human common disease, a number of relevant problems can be formulated as tests of independence. We show how defining adequate premetric structures on the support spaces of the genetic data allows for novel approaches to such testing. This yields a solid theoretical framework, which reflects the underlying biology, and allows for computationally-efficient implementations. For each problem, we provide mathematical results, simulations and the application to real data.

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