ABSTRACT

A New Way of Analyzing Object Data from a Nonparametric ViewpointNonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields

part 1|2 pages

Part I: Nonparametric Statistics on Manifolds

chapter 1|42 pages

Data on Manifolds

chapter 2|50 pages

Basic Nonparametric Multivariate Inference

chapter 3|62 pages

Geometry and Topology of Manifolds

chapter 7|18 pages

Function Estimation on Manifolds

part 2|2 pages

Part II: Asymptotic Theory and Nonparametric Bootstrap on Special Manifolds

chapter 9|6 pages

Analysis on Stiefel Manifolds

chapter 12|14 pages

Analysis on Spaces of Congruences of k-ads

chapter 13|20 pages

Similarity Shape Analysis

chapter 14|10 pages

Statistics on Grassmannians

part 3|2 pages

Part III: Applications in Object Data Analysis on Manifolds

chapter 15|12 pages

DTI Data Analysis

chapter 20|12 pages

Affine Shape and Linear Shape Applications

chapter 24|8 pages

Mean Glaucomatous Shape Change Detection

part 4|2 pages

Part IV: Additional Topics

chapter 26|16 pages

Persistent Homology