In this paper,to obtain a consistent estimator of the number of communities,the authors present a new sequential testing procedure,based on the locally smoothed adjacency matrix and the extreme value theory.Under the ...In this paper,to obtain a consistent estimator of the number of communities,the authors present a new sequential testing procedure,based on the locally smoothed adjacency matrix and the extreme value theory.Under the null hypothesis,the test statistic converges to the type I extreme value distribution,and otherwise,it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network,guaranteeing high detection power.This method is simple to use and serves as an alternative approach to the novel one in Lei(2016)using random matrix theory.To detect the change of the community structure,the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices.Simulation studies justify the theory.The authors apply the proposed method to the political blog data set and find reasonable group structures.展开更多
In this paper we investigate how to employ stochastic regression to hedge risks in finance,where the risk of a security is measured by its quadratic variation process.Mykland and Zhang used this technique to demonstra...In this paper we investigate how to employ stochastic regression to hedge risks in finance,where the risk of a security is measured by its quadratic variation process.Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security.In this paper,we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities.Some practical guidelines on how to choose those hedging securities in practice is also given.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.71971118supported by Major Natural Science Projects of Universities in Jiangsu Province under Grant No.20KJA520002。
文摘In this paper,to obtain a consistent estimator of the number of communities,the authors present a new sequential testing procedure,based on the locally smoothed adjacency matrix and the extreme value theory.Under the null hypothesis,the test statistic converges to the type I extreme value distribution,and otherwise,it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network,guaranteeing high detection power.This method is simple to use and serves as an alternative approach to the novel one in Lei(2016)using random matrix theory.To detect the change of the community structure,the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices.Simulation studies justify the theory.The authors apply the proposed method to the political blog data set and find reasonable group structures.
基金supported by Hong Kong RGC(Grant Nos.HKUST6011/07P,HKUST6015/08P)supported in part by National Natural Science Foundation of China(Grant No.10771214)
文摘In this paper we investigate how to employ stochastic regression to hedge risks in finance,where the risk of a security is measured by its quadratic variation process.Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security.In this paper,we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities.Some practical guidelines on how to choose those hedging securities in practice is also given.
