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Optimal graphon estimation in cut distance

Author

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  • Olga Klopp

    (ESSEC Business School ; CREST)

  • Nicolas Verzelen

    (INRA)

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.

Suggested Citation

  • Olga Klopp & Nicolas Verzelen, 2017. "Optimal graphon estimation in cut distance," Working Papers 2017-42, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-42
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    References listed on IDEAS

    as
    1. D. S. Choi & P. J. Wolfe & E. M. Airoldi, 2012. "Stochastic blockmodels with a growing number of classes," Biometrika, Biometrika Trust, vol. 99(2), pages 273-284.
    2. Olga Klopp & Alexandre Tsybakov & Nicolas Verzelen, 2016. "Oracle inequalities for network models and sparse graphon estimation," Working Papers 2016-13, Center for Research in Economics and Statistics.
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