Statistics and Its Interface
Volume 13 (2020)
Asymptotic Theory for Differentially Private Generalized $\beta$-models with Parameters Increasing
Pages: 385 – 398
Modelling edge weights play a crucial role in the analysis of network data, which reveals the extent of relationships among individuals. Due to the diversity of weight information, sharing these data has become a complicated challenge in a privacy-preserving way. In this paper, we consider the case of the non-denoising process to achieve the trade-off between privacy and weight information in the generalized β-model. Under the edge differential privacy with a discrete Laplace mechanism, the Z-estimators from estimating equations for the model parameters are shown to be consistent and asymptotically normally distributed. The simulations and a real data example are given to further support the theoretical results.
$\beta$-models, Discrete Laplace distribution, Edge differential privacy, Network data, Z-estimators
2010 Mathematics Subject Classification
Primary 62F12. Secondary 05C80, 62E20, 62F10.
Yan is partially supported by the National Natural Science Foundation of China (No. 11771171) and the Fundamental Research Funds for the Central Universities (No. CCNU17TS0005). Fan is supported by Fundamental Research Funds for the Central Universities (Innovative Funding Project) (2019CX ZZ071).
Received 16 April 2019
Accepted 21 February 2020
Published 22 April 2020