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 stratification arising in Statistics are considered with examples of application on data analysis and on them. Various applications include RNA based analysis of the SARSCov2 virus, 3D face identification from digital camera images, English Alphabet based comparison of certain European Languages. Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis is intended for graduate students to expand their understanding of Nonparametric Statistics, and enhance their ability to grasp and extract complex data and analysis of manifolds.

Author Biography

Vic Patrangenaru is a professor in the Statistics Department at Florida State University, Tallahassee, Florida, USA. He is an honored fellow of the Institute of Mathematical Statistics. His research encompasses analysis of complex data types, and the application of projective and differential geometry in various fields, including computer vision, medical imaging and phylogenetics. Throughout his career Dr. Patrangenaru, who guided many doctoral students, spearheaded the new area of Object Data Analysis. He added a new class to the Mathematics Subject Classification 2020 , 62R30 Statistics on Manifolds, which is currently in use by Mathematical Reviews and Zentralblatt für Mathematik

Daniel E. Osborne is an associate professor in the Mathematics Department at Florida A&M University, Tallahassee, Florida, USA. As a trained Statistician and Data Science educator, he is dedicated to training student learners and promoting best practices in data literacy, statistical reasoning, data analysis, and data visualization skills among all learners, irrespective of their backgrounds, majors, or career paths.