Optimal graphon estimation in cut distance

Olga Klopp () and Nicolas Verzelen ()
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Olga Klopp: ESSEC Business School ; CREST
Nicolas Verzelen: INRA

No 2017-42, Working Papers from Center for Research in Economics and Statistics

Abstract: We consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon function of graphon random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block constant matrices and classes of step function graphons. Surprisingly, our results imply that, from the minimax point of view, the raw data, that is the adjacency matrix of the observed graph, is already optimal and more involved procedures cannot improve the convergence rates for this metric.

Pages: 39 pages
Date: 2017-12-09
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