Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis
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Product details:
- Edition number 1
- Publisher Chapman and Hall
- Date of Publication 13 June 2025
- ISBN 9781138043138
- Binding Hardback
- No. of pages208 pages
- Size 234x156 mm
- Weight 453 g
- Language English
- Illustrations 13 Illustrations, black & white; 46 Illustrations, color; 3 Halftones, color; 13 Line drawings, black & white; 43 Line drawings, color; 3 Tables, black & white 700
Categories
Short description:
This book, a follow-up of Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis 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.
MoreLong description:
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.
Table of Contents:
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
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