Model-free Two-sample Test for Network-Valued Data

Ilenia Lovato (1) , Alessia Pini (2) , Aymeric Stamm (3) , Simone Vantini (4)

1 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]
2 Unicatt - Università cattolica del Sacro Cuore [Milano]
3 LMJL - Laboratoire de Mathématiques Jean Leray
4 MOX - Modeling and Scientific Computing [Milano]

In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In details, the present framework proceeds in four steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible $ Corresponding author alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the R package nevada (NEtwork-VAlued Data Analysis).

Mots clés: Network-valued data; Null-hypothesis testing; Object-oriented data analysis; Permutation test; Shared mobility

Domaines: Méthodologie [stat.ME]

Ilenia Lovato, Alessia Pini, Aymeric Stamm, Simone Vantini. Model-free Two-sample Test for Network-Valued Data. Computational Statistics and Data Analysis, In press. ⟨hal-02390346⟩