ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

doi:10.1007/s10473-020-0204-8

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 355-368.doi: 10.1007/s10473-020-0204-8

ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

罗敬¹, 覃红², 汪政红¹

1. Department of Statistics, South-Central University for Nationalities, Wuhan 430074, China;
2. Department of Statistics, Zhongnan University of Economics and Law, Wuhan 430073, China

收稿日期:2017-10-24 修回日期:2019-10-14 出版日期:2020-04-25 发布日期:2020-05-26
作者简介:Jing LUO,E-mail:jingluo2017@mail.scuec.edu.cn;Hong QIN,E-mail:qinhong@mail.ccnu.edu.cn;Zhenghong WANG,E-mail:wzh@mail.scuec.edu.cn
基金资助:
Luo's research is partially supported by the Fundamental Research Funds for the Central Universities (South-Central University for Nationalities (CZQ19010)), National Natural Science Foundation of China (11801576), and the Scientific Research Funds of South-Central University For Nationalities (YZZ17007); Qin's research is partially supported by National Natural Science Foundation of China (11871237); Wang's research is partially supported by the Fundamental Research Funds for the Central Universities (South-Central University for Nationalities (CZQ18017)).

ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

Jing LUO¹, Hong QIN², Zhenghong WANG¹

1. Department of Statistics, South-Central University for Nationalities, Wuhan 430074, China;
2. Department of Statistics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received:2017-10-24 Revised:2019-10-14 Online:2020-04-25 Published:2020-05-26
Supported by:
Luo's research is partially supported by the Fundamental Research Funds for the Central Universities (South-Central University for Nationalities (CZQ19010)), National Natural Science Foundation of China (11801576), and the Scientific Research Funds of South-Central University For Nationalities (YZZ17007); Qin's research is partially supported by National Natural Science Foundation of China (11871237); Wang's research is partially supported by the Fundamental Research Funds for the Central Universities (South-Central University for Nationalities (CZQ18017)).

摘要/Abstract

摘要： The asymptotic normality of the fixed number of the maximum likelihood estimators (MLEs) in the directed finite weighted network models with an increasing bi-degree sequence has been established recently. In this article, we further derive the central limit theorem for linear combinations of all the MLEs with an increasing dimension when the edges take finite discrete weight. Simulation studies are provided to illustrate the asymptotic results.

关键词: Central limit theorem, finite discrete network, increasing number of parameters, maximum likelihood estimator

Abstract: The asymptotic normality of the fixed number of the maximum likelihood estimators (MLEs) in the directed finite weighted network models with an increasing bi-degree sequence has been established recently. In this article, we further derive the central limit theorem for linear combinations of all the MLEs with an increasing dimension when the edges take finite discrete weight. Simulation studies are provided to illustrate the asymptotic results.

Key words: Central limit theorem, finite discrete network, increasing number of parameters, maximum likelihood estimator

中图分类号:

62E20

罗敬, 覃红, 汪政红. ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE[J]. 数学物理学报(英文版), 2020, 40(2): 355-368.

Jing LUO, Hong QIN, Zhenghong WANG. ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE[J]. Acta mathematica scientia,Series B, 2020, 40(2): 355-368.

参考文献

[1] Agneessens F, Roose H, Waege H. Choices of theatre events:p^* models for affiliation networks with attributes. Metodoloski Zvezki, 2004, 1:419-439
[2] Battiston S, Catanzaro M. Statistical properties of corporate board and director networks. The European Physical Journal B-Condensed Matter and Complex Systems, 2004, 38(2):345-352
[3] Bickel P J, Chen A, Levina E, et al. The method of moments and degree distributions for network models. The Annals of Statistics, 2011, 39(5):2280-2301
[4] Billingsley P. Convergence of probability measures. John Wiley & Sons, 1968
[5] Blitzstein J, Diaconis P. A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Internet Mathematics, 2011, 6(4):489-522
[6] Britton T, Deijfen M, Martin-Löf A. Generating simple random graphs with prescribed degree distribution. Journal of Statistical Physics, 2006, 124(6):1377-1397
[7] Chatterjee S, Diaconis P, Sly A. Random graphs with a given degree sequence. The Annals of Applied Probability, 2011, 21(4):1400-1435
[8] Darmois G. Sur les lois de probabilitéa estimation exhaustive. CR Acad Sci Paris, 1935, 260(1265):85
[9] Ergün G. Human sexual contact network as a bipartite graph. Physica A:Statistical Mechanics and its Applications, 2002, 308(1):483-488
[10] Fienberg S E. A brief history of statistical models for network analysis and open challenges. Journal of Computational and Graphical Statistics, 2012, 21(4):825-839
[11] Freeman L C, Webster C M, Kirke D M. Exploring social structure using dynamic three-dimensional color images. Social Networks, 1998, 20(2):109-118
[12] Freeman S, Freeman L. The networkers network:A study of the impact of a new communications medium on sociometric structure//Social Science Research Reports 46. Irvine, CA:University of California, 1979
[13] Hillar C, Wibisono A. Maximum entropy distributions on graphs. arXiv:1301.3321, 2013
[14] Holland P W, Leinhardt S. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 1981, 76(373):33-50
[15] Koopman B O. On distributions admitting a sufficient statistic. Transactions of the American Mathematical Society, 1936, 39(3):399-409
[16] Luo J, Qin H, Yan T, Zeyneb L. A note on asymptotic distributions in directed exponential random graph models with bi-degree sequences. Communications in Statistics-Theory and Methods, 2017, 46(18):8852-8864
[17] Newman M E. Scientific collaboration networks. I. network construction and fundamental results. Physical Review E, 2001, 64(1):016131
[18] Pitman E J G. Sufficient statistics and intrinsic accuracy//Mathematical Proceedings of the cambridge Philosophical society. Cambridge Univ Press, 1936, 32:567-579
[19] Rinaldo A, Petrović S, Fienberg S E. Maximum lilkelihood estimation in the beta-model. The Annals of Statistics, 2013, 41(3):1085-1110
[20] Skvoretz J, Faust K. Logit models for affiliation networks. Sociological Methodology, 2002, 29(1):253-280
[21] Snijders T A, Lomi A, Torló V J. A model for the multiplex dynamics of two-mode and one-mode networks, with an application to employment preference, friendship, and advice. Social Networks, 2013, 35(2):265-276
[22] Wang P, Sharpe K, Robins G L, Pattison P E. Exponential random graph (p^*) models for affiliation networks. Social Networks, 2009, 31(1):12-25
[23] Watts D J, Strogatz S H. Collective dynamics of small-world networks. Nature, 1998, 393(6684):440-442
[24] Yan T, Leng C, Zhu J. Asymptotics in directed exponential random graph models with an increasing bi-degree sequence. The Annals of Statistics, 2016, 44(1):31-57
[25] Yan T, Qin H, Wang H. Asymptotics in undirected random graph models parameterized by the strengths of vertices. Statistica Sinica, 2016, 26(1):273-293
[26] Yan T, Xu J. A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices. Biometrika, 2013, 100(2):519-524
[27] Yong Z, Chen S, Qin H, Yan T. Directed weighted random graphs with an increasing bi-degree sequence. Statistics and Probability Letters, 2016, 119:235-240
[28] Zhang H, Liu Y, Li B. Notes on discrete compound poisson model with applications to risk theory. Insurance Mathematics and Economics, 2014, 59:325-336
[29] Zhao Y, Levina E, Zhu J. Consistency of community detection in networks under degree-corrected stochastic block models. The Annals of Statistics, 2012, 40(4):2266-2292

ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

Metrics

本文评价

推荐阅读 0

[1]	孙建强\|丁义明. RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM[J]. 数学物理学报(英文版), 2015, 35(1): 79-88.
[2]	高志强, 刘全升, 汪和松. CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME[J]. 数学物理学报(英文版), 2014, 34(2): 501-512.
[3]	高振龙, 胡晓予. LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT[J]. 数学物理学报(英文版), 2012, 32(3): 1193-1205.
[4]	胡耀忠, Nualart David, 肖炜麟, 张卫国. EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION[J]. 数学物理学报(英文版), 2011, 31(5): 1851-1859.
[5]	夏红强, 檀大耀. A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS[J]. 数学物理学报(英文版), 2011, 31(3): 1123-1132.
[6]	毛明志, 李志民. ASYMPTOTIC BEHAVIOR FOR RANDOM WALK IN RANDOM \|ENVIRONMENT WITH HOLDING TIMES[J]. 数学物理学报(英文版), 2010, 30(5): 1696-1708.
[7]	夏红强. LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS[J]. 数学物理学报(英文版), 2010, 30(3): 701-712.
[8]	宋凤丽; 刘禄勤. A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION[J]. 数学物理学报(英文版), 2008, 28(3): 501-512.
[9]	杨乔华; 张钦. THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))[J]. 数学物理学报(英文版), 2007, 27(4): 867-874.
[10]	林正炎. ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE[J]. 数学物理学报(英文版), 2003, 23(3): 345-.
[11]	龙红卫. ON THE RATES OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR TWO-PARAMETER MARTINGALE DIFFERENCES[J]. 数学物理学报(英文版), 1996, 16(3): 287-295.