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

1st Edition

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

By Victor Patrangenaru, Daniel E. Osborne Copyright 2025
204 Pages 46 Color & 13 B/W Illustrations
by Chapman & Hall

204 Pages 46 Color & 13 B/W Illustrations
by Chapman & Hall
Also available as eBook on:
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,... Read more

Foreword 

Preface  

Part 1: Data and Preliminares for Analysis on Stratified Spaces  

1. Data of Complex Type 

2. Review of Nonparametric Statistics on Manifolds  

Part 2: Nonparametric Statistics on Stratified Spaces  

3. Spaces with a Manifold Stratification 

4. Extrinsic Data Analysis on Stratified Spaces 

5. Intrinsic Sample Means on Tree Spaces 

6. Central Limit Theorem for Random Samples on a Graph 

7. Analysis of Magnetic Resonance Angiography Data 

8. An Application to Phylogenies of SARS-CoV-2 Data Analysis  

Part 3: Asymptotic Theory and Nonparametric Bootstrap on Special Stratified Spaces   

9. CLT on Low Dimensional Stratified Spaces 

10. Investigating Two Possible Origins of SARS-CoV-2 

11. Applications of Tree Spaces to Language Ancestry 

12. 3D Face Differentiation from Digital Camera Images 

13. Further Directions in Statistics on Stratified Spaces  Bibliography

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.

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