Directed weighted random graphs with an increasing bi-degree sequence. (English) Zbl 1351.62068
Summary: In this paper, we derive the consistency and asymptotic normality of the maximum likelihood estimator in the directed exponential random graph model with an increasing bi-degree sequence when the edges take finite discrete weight.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
consistency; asymptotic normality; directed network; finite discrete weight; maximum likelihood estimatorSoftware:
MCODEReferences:
| [1] | Amaral, L. A.N.; Scala, A.; Barthelemy, M.; Stanley, H. E., Classes of small-world networks, Proc. Natl. Acad. Sci., 97, 21, 11149-11152, (2000) |
| [2] | Bader, G. D.; Hogue, C. W., An automated method for finding molecular complexes in large protein interaction networks, BMC Bioinformatics, 4, 1, 2, (2003) |
| [3] | Bernard, H. R.; Killworth, P.; Sailer, L., Informant accuracy in social network data V, Soc. Sci. Res., 11, 30-66, (1982) |
| [4] | Bickel, P. J.; Chen, A.; Levina, E., The method of moments and degree distributions for network models, Ann. Statist., 39, 5, 2280-2301, (2011) · Zbl 1232.91577 |
| [5] | Chatterjee, S.; Diaconis, P.; Sly, A., Random graphs with a given degree sequence, Ann. Appl. Probab., 21, 1400-1435, (2011) · Zbl 1234.05206 |
| [6] | Chung, F.; Lu, L., The average distances in random graphs with given expected degrees, Proc. Natl. Acad. Sci. USA, 99, 15879-15882, (2002) · Zbl 1064.05137 |
| [7] | Fienberg, S. E.; Rinaldo, A., Maximum likelihood estimation in log-linear models, Ann. Statist., 40, 996-1023, (2012) · Zbl 1274.62389 |
| [8] | Freeman, S. C.; Freeman, L. C., The networkers network: A study of the impact of a new communications medium on sociometric structure. social science research reports no 46, (1979), University of California Irvine, CA |
| [9] | Haberman, S. J., The analysis of frequency data, (1974), University of Chicago Press Chicago · Zbl 0325.62017 |
| [10] | Hillar, C., Wibisono, A., 2013. Maximum entropy distributions on graphs. ArXiv Preprint. arXiv:1301.3321. |
| [11] | Holland, P. W.; Leinhardt, S., An exponential family of probability distributions for directed graphs (with discussion), J. Amer. Statist. Assoc., 76, 33-65, (1981) · Zbl 0457.62090 |
| [12] | Newman, M. E., The structure of scientific collaboration networks, Proc. Natl. Acad. Sci., 98, 2, 404-409, (2001) · Zbl 1065.00518 |
| [13] | Olhede, S.C., Wolfe, P.J., 2012. Degree-based network models. Available at http://arxiv.org/abs/1211.6537. |
| [14] | Perry, P.O., Wolfe, P.J., 2012. Null models for network data. Available at http://arxiv.org/abs/1201.5871. |
| [15] | Rinaldo, A.; Petrović, S.; Fienberg, S. E., Maximum lilkelihood estimation in the \(\beta \)-model, Ann. Statist., 41, 3, 1085-1110, (2013) · Zbl 1292.62052 |
| [16] | Yan, T., A note on asymptotic distributions in maximum entropy models for networks, Statist. Probab. Lett., 98, 1-5, (2015) · Zbl 1321.62017 |
| [17] | Yan, T.; Leng, C.; Zhu, J., Asymptotics in directed exponential random graph models with an increasing bi-degree sequence, Ann. Statist., 44, 31-57, (2016) · Zbl 1331.62110 |
| [18] | Yan, T.; Xu, J., A central limit theorem in the \(\beta \)-model for undirected random graphs with a diverging numbeccmdr of vertices, Biometrika, 100, 519-524, (2013) · Zbl 1452.62214 |
| [19] | Yan, T.; Zhao, Y.; Qin, H., Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters, J. Multivariate Anal., 133, 61-76, (2015) · Zbl 1304.62038 |
| [20] | Zhao, Y.; Levina, E.; Zhu, J., Consistency of community detection in networks under degree-corrected stochastic block models, Ann. Statist., 40, 2266-2292, (2012) · Zbl 1257.62095 |
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