Paper Info
Title
Model-free two-sample test for network-valued data.
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).
Year
DOI
Venue
2020
10.1016/j.csda.2019.106896
Computational Statistics & Data Analysis
Keywords
Field
DocType
Network-valued data,Null-hypothesis testing,Object-oriented data analysis,Permutation test,Shared mobility
Pairwise comparison,Statistic,Matrix (mathematics),Permutation,Algorithm,Statistics,Resampling,Statistical power,Matrix representation,Statistical hypothesis testing,Mathematics
Journal
Volume
ISSN
Citations 
144
0167-9473
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Ilenia Lovato100.34
Alessia Pini262.55
Aymeric Stamm3113.76
Simone Vantini4609.26