Model-free two-sample test for network-valued data

Alessia Pini, Ilenia Lovato, Aymeric Stamm, Simone Vantini

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In detail, 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 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).
Original languageEnglish
Pages (from-to)N/A-N/A
JournalCOMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume144
DOIs
Publication statusPublished - 2020

Keywords

  • Network-valued data
  • Null-hypothesis testing
  • Object-oriented data analysis
  • Permutation test
  • Shared mobility

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