Metric sample spaces of continuous geometric curves and estimation of their centroids (Q2762656)

Let us consider a metric space of Fréchet curves which is based on a generalization of regular curves that covers continuous curves in full generality. In the present paper this sample space is further extended in two directions that are relevant in practice: to incorporate information on landmark points in the curves and to impose invariance with respect to an arbitrary group of isometric spatial transformations. Properties of the introduced sample spaces of curves are studied, specially those concerning the generation and representation of random curves by random functions. In order to provide measures of central tendency and dispersions of random curves, centroids and restricted centroids of random curves are defined in general metric framework, and methods for their consistent estimation are derived.