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Asymptotic behavior of parameter estimators and test statistics for graphs

Grant number: 17/12074-0
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): November 27, 2017
Effective date (End): March 26, 2018
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computational Mathematics
Principal Investigator:André Fujita
Grantee:Suzana de Siqueira Santos
Supervisor abroad: Catherine Matias
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Local de pesquisa : Université Pierre et Marie Curie (Paris 6), France  
Associated to the scholarship:15/21162-4 - Identification of variables associated with the graph structure and applications in neuroscience, BP.DR

Abstract

Graph theory has applications in several domains. For example, in molecular biology graphs may represent protein-protein interaction networks or gene regulatory networks; and in neuroscience they are used to study brain functional networks. As real world networks usually present intrinsic fluctuations (for example, brain functional networks vary across time and individuals under the same condition), their representation by deterministic graphs is not adequate. An alternative is to assume that real world networks are generated by probabilistic processes and model them by using random graph models. The problem is that little is known about statistical methods for random graphs. Recently, statistical approaches have been proposed to (i) estimate the parameters of a random graph model (parameter estimation); and (ii) to test whether sets of graphs were generated by the same graph model and set of parameters. However, the asymptotic behavior of these methods are still unknown. Furthermore, the original approach for (ii) is based on bootstrap and thus presents a high computational cost. Therefore, here we propose to derive the asymptotic behavior of the parameter estimator in (i) and to create an analytic test for (ii).To achieve these goals, this candidate will work for four months under the supervision of Prof. Catherine Matias (Université Pierre et Marie Curie, France), who has over 10 years of experience on statistical methods for random graphs.