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Parametric and Nonparametric Spherical Regression with Diffeomorphisms

Title: Parametric and Nonparametric Spherical Regression with Diffeomorphisms.
Name(s): Rosenthal, Michael, author
Srivastava, Anuj, professor co-directing dissertation
Wu, Wei, professor co-directing dissertation
Klassen, Eric, university representative
Pati, Debdeep, committee member
Department of Statistics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2014
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Spherical regression explores relationships between pairs of variables on spherical domains. Spherical data has become more prevalent in biological, gaming, geographical, and meteorological investigations, creating a need for tools that analyze such data. Previous works on spherical regression have focused on rigid parametric models or nonparametric kernel smoothing methods. This leaves a huge gap in the available tools with no intermediate options currently available. This work will develop two such intermediate models, one parametric using projective linear transformation and one nonparametric model using diffeomorphic maps from a sphere to itself. The models are estimated in a maximum-likelihood framework using gradient-based optimizations. For the parametric model, an efficient Newton-Raphson algorithm is derived and asymptotic analysis is developed. A first-order roughness penalty is specified for the nonparametric model using the Jacobian of diffeomorphisms. The prediction performance of the proposed models are compared with state-of-the-art methods using simulated and real data involving plate tectonics, cloud deformations, wind, accelerometer, bird migration, and vector-cardiogram data.
Identifier: FSU_migr_etd-9082 (IID)
Submitted Note: A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2014.
Date of Defense: June 5, 2014.
Keywords: Diffeomorphism, Manifold, Nonlinear Regression, Projective Linear Transformation, Riemannian Geometry, Spherical Regression
Bibliography Note: Includes bibliographical references.
Advisory Committee: Anuj Srivastava, Professor Co-Directing Dissertation; Wei Wu, Professor Co-Directing Dissertation; Eric Klassen, University Representative; Debdeep Pati, Committee Member.
Subject(s): Statistics
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Owner Institution: FSU

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Rosenthal, M. (2014). Parametric and Nonparametric Spherical Regression with Diffeomorphisms. Retrieved from