Nonparametric Statistics on Manifolds and Their Applications

Requiring only a background in mathematical statistics or analysis, this book provides the first comprehensive look at the statistics of manifolds. It presents location and spread parameters for distribution on manifolds, followed by key large sample theory results. The text also addresses inference of two samples, nonparametric MANOVA, principal component analysis, and density estimation on manifolds. A special section is dedicated to a nonparametric statistical analysis on certain special manifolds arising in statistics. The final part of the text focuses on concrete applications in astronomy, image analysis, medical imaging, bioinformatics, and pattern recognition.