Abstract
We formulate a model for the off-line estimation of a changepoint in a network setting. The framework naturally allows the parameter space (network size) to grow with the number of observations. We compute the signal-to-noise ratio detectability threshold, and establish the dependence of the rate of convergence and asymptotic distribution on the network size and parameters. In addition, we show that inference can be adaptive, i.e. asymptotically correct confidence intervals can be computed based on the data. We apply the method to the question of whether US Congress has abruptly become more polarized at some point in recent history.
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Acknowledgements
E.Y.’s research was partially supported by US NSF grant DMS-1204311. M.B.’s research was partially supported by US NSF DMS-1007751, US NSA H98230-11-1-0166, and a Sokol Faculty Award, University of Michigan. G.M.’s research was partially supported by US NSF DMS-1228164 and US NSA H98230-13-1-0241. The authors thank the referees for helpful comments.
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Yudovina, E., Banerjee, M., Michailidis, G. (2015). Changepoint Inference for Erdős–Rényi Random Graphs. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_22
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DOI: https://doi.org/10.1007/978-3-319-13881-7_22
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