Separability of stochastic processes

Testing separability of space–time functional processes

We present a new methodology and accompanying theory to test for separability of spatio–temporal functional data. In spatio–temporal statistics, separability is a common simplifying assumption concerning the covariance structure which, if true, can greatly increase estimation accuracy and inferential power. While our focus is on testing for the separation of space and time in spatio-temporal da...

A Useful Family of Stochastic Processes for Modeling Shape Diffusions

 One of the new area of research emerging in the field of statistics is the shape analysis. Shape is defined as all the geometrical information of an object whose location, scale and orientation is not of interest. Diffusion in shape analysis can be studied via either perturbation of the key coordinates identifying the initial object or random evolution of the shape itself. Reviewing the f...

On the Separability of Stochastic Geometric Objects, with Applications

In this paper, we study the linear separability problem for stochastic geometric objects under the wellknown unipoint/multipoint uncertainty models. Let S = SR∪SB be a given set of stochastic bichromatic points, and define n = min{|SR|, |SB |} and N = max{|SR|, |SB |}. We show that the separable-probability (SP) of S can be computed in O(nNd−1) time for d ≥ 3 and O(min{nN logN,N}) time for d = ...

Material for ” Testing separability of space - time functional processes ”

This Supplementary Material contains mostly proofs of the large sample results used in the paper. However, we begin with the detailed description of testing procedures which do not involve spatial dimension reduction, Section A. Then, in Section B, we proceed with the derivation of the form of several matrices which are needed to formulate the joint asymptotic distribution of the maximum likeli...

Stochastic Processes