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

TL;DR

This paper develops novel nonparametric independence tests tailored for high-dimensional genetic data, offering a robust theoretical framework, efficient algorithms, and applications to complex disease genetics.

Contribution

It introduces a new approach using premetric structures for independence testing in high-dimensional genetics, combining theoretical insights with practical implementations.

Findings

The proposed tests are computationally efficient.

The methods outperform existing tests in simulations.

Applications to real genetic data demonstrate effectiveness.

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.