Statistical Inference Research With Differential Privacy Networks Model

With the advent of the era of big data,the issue of privacy protection has be-come a hot topic in the statistical analysis of network data.Differential privacy is a commonly used method in privacy protection.Within this framework,a series of algorithms have been proposed and developed,but statistical inference for data with privacy remains a challenge.In particular,Chatterjee et al.(2011)proposed the βnetwork model,where the degree sequence is a sufficient statistic for the model.In this paper,we estimate the parameters of the β network model with noise by the moment estimation method,and propose statistical inference of the differential privacy estimators.The main results are as follows:First,we estimate the differ-ential privacy parameters by the moment estimation method;Second,we study the consistency of the differential privacy estimators;Third,we study the asymptotic normality of the differential privacy estimators;Finally,we verify the asymptotic normality of the differential privacy estimators through numerical simulations and practical examples.