Title: Statistical inference on stratified manifolds
Authors: Charles Xi Yan - University of Nottingham (United Kingdom) [presenting]
Abstract: Stratified manifolds are metric spaces consisting of strata of different dimensions that are ``stuck together'' suitably. One type of stratified space is the so-called open book, the simplest of which is the 3-Spider. An important area of application of stratified spaces is to random tree structures, such as phylogenetic trees. However, it is not easy to construct parametric models on stratified manifolds. For this reason, a non-parametric approach to inference based on empirical likelihood has been investigated. By bootstrap replicates and bootstrap calibration, confidence regions can be constructed. To further the study, the core of such an inference, Wilk's Theorem, on different manifolds is introduced. Wilk's theorem has been proved by Owen on the Euclidean Space. Empirical likelihood is also applied to a second example, the unit sphere. By considering the extrinsic mean and intrinsic mean, Wilk's Theorem is proved again.