Asymptotic theory in a class of directed random graph models with a differentially private bi-degree sequence

01/24/2022

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by   Lu Pan, et al.

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Although the asymptotic properties of the parameter estimator have been derived in the p_0 model for directed graphs with the differentially private bi-degree sequence, asymptotic theory in general models is still lacking. In this paper, we release the bi-degree sequence of directed graphs via the discrete Laplace mechanism, which satisfies differential privacy. We use the moment method to estimate the unknown model parameter. We establish a unified asymptotic result, in which consistency and asymptotic normality of the differentially private estimator holds. We apply the unified theoretical result to the Probit model. Simulations and a real data demonstrate our theoretical findings.