Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis

This book, a follow-up of Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis where the reader was introduced to data analysis on manifolds, is expanding the subject of data analysis on object spaces, to the case of metric spaces that have a smooth structure on an open dense subset only, governed by a nice filtration structure on the singular part of this space, that is comprised of manifolds whose boundaries are made of lower dimensional manifolds in this filtration.Such object spaces are known as stratified spaces, and their structure will be detailed in the second part of the book.Key examples of complex data from which one extracts data representable as points on a stratified space, and a review on data analysis on manifolds, are provided, alongside a summary of results on nonparametric methods on manifolds.Key results on asymptotic and nonparametric bootstrap on some stratified spaces are included.Certain object spaces with a manifold stratificatio