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

doi:10.1007/s10473-020-0204-8

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (2): 355-368.doi: 10.1007/s10473-020-0204-8

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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)).

Abstract

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

CLC Number:

62E20

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.

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

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