Parametric and Non-parametric Testing of Mean Shapes

Abstract

This chapter deals with inferential aspects in shape analysis. At first we review inferential methods known in the shape analysis literature, highlighting some drawbacks of using Hotelling’s T2 test statistic. Then we present an extension of the NonParametric Combination (NPC) methodology to compare shape configurations of landmarks. NPC tests represent an appealing alternative since they are distribution-free and allow for quite efficient solutions when the number of cases is lower than the number of variables (i.e., (semi)landmarks coordinates). This allows to obtain better representations of shapes even in presence of small sample size. NPC methodology enables to provide global as well as local evaluation of shapes: it is then possible to establish whether in general two shapes are different and which landmark/subgroup of landmarks mainly contributes to differentiate shapes under study. NPC tests enjoy the finite-sample consistency property hence, in this nonparametric framework, it is possible to obtain efficient solutions for multivariate small sample problems, like those encountered in the shape analysis field. We finally present a NPC solution for longitudinal data.