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May 2019 A Kernel Regression Procedure in the 3D Shape Space with an Application to Online Sales of Children’s Wear
Gregorio Quintana-Ortí, Amelia Simó
Statist. Sci. 34(2): 236-252 (May 2019). DOI: 10.1214/18-STS675

Abstract

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.

Citation

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Gregorio Quintana-Ortí. Amelia Simó. "A Kernel Regression Procedure in the 3D Shape Space with an Application to Online Sales of Children’s Wear." Statist. Sci. 34 (2) 236 - 252, May 2019. https://doi.org/10.1214/18-STS675

Information

Published: May 2019
First available in Project Euclid: 19 July 2019

zbMATH: 07110695
MathSciNet: MR3983327
Digital Object Identifier: 10.1214/18-STS675

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.34 • No. 2 • May 2019
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