Empirical likelihood in Euclidean and some non-Euclidean spaces - Yan, Xi (2020)
Empirical likelihood is a non-parametric approach to statistical inference which bears some resemblance to parametric approaches and yet avoids making parametric assumptions. The aim of this thesis is to develop theoretical and computational aspects of empirical likelihood when applied to data from two different types of non-Euclidean space. The two spaces we focus on are the sphere, which is an important example of a manifold with non-Euclidean structure and is the appropriate sample space in directional statistics; and the 3-Spider, which is an example of a stratified manifold. The focus is mainly on developing empirical likelihood for a Fréchet mean in these two settings. Key achievements are: to prove versions of Wilks’ theorem which open the way to the application of methods of inference including the construction of confidence regions and hypothesis testing; and the development of algorithms for performing the computations.