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    Local linear graphon estimation using covariates

    Chandna, Swati and Olhede, S. and Wolfe, P. (2021) Local linear graphon estimation using covariates. Biometrika , ISSN 1464-3510. (In Press)

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    Abstract

    We consider local linear estimation of the graphon function which determines probabilities of pairwise edges between nodes within an unlabeled network. Real world networks are typically characterized by node heterogeneity with different nodes exhibiting different degrees of interaction. Existing approaches to graphon estimation are limited to local constant approximations, and are not designed to estimate heterogeneity across the full network. In this paper, we show how continuous node covariates can be employed to estimate heterogeneity in the network via a local linear graphon estimator. We derive the bias and variance of an oracle based local linear graphon estimator and thus obtain the mean integrated squared error optimal bandwidth rule. We also provide a plug-in bandwidth selection procedure, making local linear estimation for unlabeled networks practically feasible. Finite sample performance is investigated in a simulation study. We apply our method to a school friendship network and an email network to illustrate the advantages offered by our approach over existing methods.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): Exchangeable network, Graph limit, Graphon estimation, Nonparametric regression
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Swati Chandna
    Date Deposited: 17 Jan 2022 07:53
    Last Modified: 20 Jan 2022 04:15
    URI: https://eprints.bbk.ac.uk/id/eprint/47271

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