Nonparametric Spherical Regression Using Diffeomorphic Mappings

• Activity Number: 610
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael Rosenthal*+ and Wei Wu and Eric Klassen and Anuj Srivastava
• Companies: Florida State University and Florida State University and Florida State University and Florida State University
• Keywords: Spherical Regression ; Nonparametric ; Diffeomorphism ; Roughness Measure

Abstract

The analysis of paired spherical data has applications in many fields. A majority of the past works on spherical regression have primarily been limited to parametric forms. We develop a nonparametric spherical regression model where the conditional mean is given by a diffeomorphic map from a sphere to itself. We perform model estimation under penalized likelihood which we maximize using a gradient approach. Towards that goal we specify a first order roughness penalty using the Jacobian map of diffeomorphisms. We demonstrate these ideas using simulated and real data involving plate tectonics and cloud deformations.