文章基本信息

标题：On a complete and sufficient statistic for the correlated Bernoulli random graph model
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作者：Donniell E. Fishkind ; Avanti Athreya ; Lingyao Meng 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：1
页码：2336-2359
DOI：10.1214/21-EJS1839
语种：English
出版社：Institute of Mathematical Statistics
摘要：Inference on vertex-aligned graphs is of wide theoretical and practical importance. There are, however, few flexible and tractable statistical models for correlated graphs, and even fewer comprehensive approaches to parametric inference on data arising from such graphs. In this paper, we consider the correlated Bernoulli random graph model (allowing different Bernoulli coefficients and edge correlations for different pairs of vertices), and we introduce a new variance-reducing technique—called balancing—that can refine estimators for model parameters. Specifically, we construct a disagreement statistic and show that it is complete and sufficient; balancing can be interpreted as Rao-Blackwellization with this disagreement statistic. We show that for unbiased estimators of functions of model parameters, balancing generates uniformly minimum variance unbiased estimators (UMVUEs). However, even when unbiased estimators for model parameters do not exist—which, as we prove, is the case with both the heterogeneity correlation and the total correlation parameters—balancing is still useful, and lowers mean squared error. In particular, we demonstrate how balancing can improve the efficiency of the alignment strength estimator for the total correlation, a parameter that plays a critical role in graph matchability and graph matching runtime complexity.
关键词：62B05; 62F10; alignment strength; Graph matching; Lehmann-Scheffé; Rao-Blackwell; total correlation (graph)