THE METHOD OF MOMENTS AND DEGREE DISTRIBUTIONS FOR NETWORK MODELS

被引：126

作者：

Bickel, Peter J. ^{[1
]}

Chen, Aiyou ^{[2
]}

Levina, Elizaveta ^{[3
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

[2] Google Inc, Mountain View, CA 94043 USA

[3] Univ Michigan, Dept Stat, Ann Arbor, MI 48109 USA

来源：

ANNALS OF STATISTICS | 2011年 / 39卷 / 05期

基金：

美国国家科学基金会;

关键词：

Social networks; block model; community detection; STOCHASTIC BLOCKMODELS; PREDICTION;

D O I：

10.1214/11-AOS904

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including Omega (1). Additional results are obtained for the important special case of degree distributions.

引用

页码：2280 / 2301

页数：22

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