Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

Abstract.

For differential privacy under sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this article, we release the degree sequences of the binary networks under a general noisy mechanism, with the discrete Laplace mechanism as a special case. We establish the asymptotic result, including both consistency and asymptotically normality, of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real-data example are provided to illustrate the asymptotic results.

Keywords:

• Consistency and asymptotic normality
• network data
• differential privacy
• sub-Gamma degree sequence

Mathematics Subject Classification 2020::

• 62E20
• 62F12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Luo’s research is partially supported by the Fundamental Research Funds for the Central Universities of South-Central Minzu University (Grant Number: CZQ22003) and by National Statistical Science Research of China (2022LY051) and by the Open Research Fund of Key Laboratory of Non linear Analysis and Applications (Central China Normal University), Ministry of Education, P.R. China.