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Nonparametric graphon estimation

Wolfe, PJ; Olhede, SC; Nonparametric graphon estimation.

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Abstract

We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical setting of sparse networks. Our results cover dense and sparse stochastic blockmodels with a growing number of classes, under model misspecification. We use profile likelihood methods, and connect our results to approximation theory, nonparametric function estimation, and the theory of graph limits.

Type: Article
Title: Nonparametric graphon estimation
Additional information: 52 pages; submitted for publication
Keywords: math.ST, math.ST, math.CO, math.PR, stat.TH, 62G05 (Primary) 05C80, 62G20 (Secondary)
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/1409022
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