A kernel regression procedure in the 3D shape space with an application to online sales of children's wear

Abstract

Shape regression is of key importance in many scienti c elds. In this paper, we focus on the case where the shape of an object is represented by a con- guration matrix of landmarks. It is well known that this shape space has a nite-dimensional Riemannian manifold structure (non-Euclidean) which makes it di cult to work with. Papers about regression on this space are scarce in the literature. The majority of them are restricted to the case of a single explanatory variable, usually time or age, and many of them work in the approximated tangent space. In this paper we adapt the general method for kernel regression analysis in manifold-valued data proposed by Davis et al (2007) to the three-dimensional case of Kendall's shape space and generalize it to multiple explanatory variables. We also propose bootstrap con dence intervals for prediction. A simulation study is carried out to check the goodness of the procedure, and nally 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.