A Kernel Regression Procedure in the 3D Shape Space with an Application to Online Sales of Children's Wear

This paper is focused on kernel regression when the response variable is the shape of a 3D object represented by a configuration matrix of landmarks. Regression methods on this shape space are not trivial because this space has a complex finite-dimensional Riemannian manifold structure (non-Euclidea...

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Bibliographic Details
Published in:Statistical science 2019-05, Vol.34 (2), p.236-252
Main Authors: Quintana-Ortí, Gregorio, Simó, Amelia
Format: Article
Language:English
Subjects:
Anthropometry
Confidence intervals
Euclidean geometry
Kernels
Manifolds (mathematics)
Multivariate analysis
Regression analysis
Riemann manifold
Sales
Simulation
Statistical analysis
Three dimensional imaging
Wear
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Summary:This paper is focused on kernel regression when the response variable is the shape of a 3D object represented by a configuration matrix of landmarks. Regression methods on this shape space are not trivial because this space has a complex finite-dimensional Riemannian manifold structure (non-Euclidean). Papers about it are scarce in the literature, the majority of them are restricted to the case of a single explanatory variable, and many of them are based on the approximated tangent space. In this paper, there are several methodological innovations. The first one is the adaptation of the general method for kernel regression analysis in manifold-valued data to the three-dimensional case of Kendall's shape space. The second one is its generalization to the multivariate case and the addressing of the curse-of-dimensionality problem. Finally, we propose bootstrap confidence intervals for prediction. A simulation study is carried out to check the goodness of the procedure, and a comparison with a current approach is performed. Then, it is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children's wear.
ISSN:0883-4237
2168-8745
DOI:10.1214/18-STS675