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Local linear graphon estimation using covariates
[Representations for partially exchangeable arrays of random variables]

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  • S Chandna
  • S C Olhede
  • P J Wolfe

Abstract

SummaryWe consider local linear estimation of the graphon function, which determines probabilities of pairwise edges between nodes in an unlabelled 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 that makes local linear estimation for unlabelled networks practically feasible. The finite-sample performance of our approach is investigated in a simulation study, and the method is applied to a school friendship network and an email network to illustrate its advantages over existing methods.

Suggested Citation

  • S Chandna & S C Olhede & P J Wolfe, 2022. "Local linear graphon estimation using covariates [Representations for partially exchangeable arrays of random variables]," Biometrika, Biometrika Trust, vol. 109(3), pages 721-734.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:3:p:721-734.
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    References listed on IDEAS

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    1. Bailey K. Fosdick & Peter D. Hoff, 2015. "Testing and Modeling Dependencies Between a Network and Nodal Attributes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1047-1056, September.
    2. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    3. Patrick O. Perry & Patrick J. Wolfe, 2013. "Point process modelling for directed interaction networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 821-849, November.
    4. Hardle, W. & Marron, J. S., 1995. "Fast and simple scatterplot smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 1-17, July.
    5. Yuan Zhang & Elizaveta Levina & Ji Zhu, 2017. "Estimating network edge probabilities by neighbourhood smoothing," Biometrika, Biometrika Trust, vol. 104(4), pages 771-783.
    6. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    7. Ting Yan & Binyan Jiang & Stephen E. Fienberg & Chenlei Leng, 2019. "Statistical Inference in a Directed Network Model With Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 857-868, April.
    8. N. Binkiewicz & J. T. Vogelstein & K. Rohe, 2017. "Covariate-assisted spectral clustering," Biometrika, Biometrika Trust, vol. 104(2), pages 361-377.
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