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Explore empirical likelihood methods for statistical inference on Fréchet means within open book spaces, a fundamental example of stratified geometric structures. Learn how open books serve as simplified models that capture key properties of stratified spaces while maintaining mathematical tractability. Discover the central limit theory framework for open books as established by Hotz et al. (2013), providing essential background for understanding statistical behavior in these geometric settings. Examine how empirical likelihood, a nonparametric approach developed by Owen (2001), can be effectively applied to manifold-valued and stratified space data. Understand the construction of basic inference procedures for Fréchet means using empirical likelihood methods, with particular attention to how geometric non-regularity in open books leads to non-standard behavior in Wilks's theorem for large sample likelihood ratio tests. Investigate the challenges and limitations when extending empirical likelihood inference theory from open books to more complex stratified spaces, especially when adjacent strata differ by two or more dimensions. Consider connections to orthant spaces as discussed by Barden and Le (2018) and the broader stratified space framework developed by Mattingly et al. (2023), highlighting the ongoing research directions in geometric statistics for complex data structures.
