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

TL;DR

This paper investigates the asymptotic behavior of a broad class of binary network models under differential privacy constraints, specifically with sub-Gamma noise, and establishes key statistical properties of parameter estimators.

Contribution

It introduces a general framework for analyzing binary network models with increasing parameters under sub-Gamma noise, including the discrete Laplace mechanism, and proves estimator consistency and normality.

Findings

Establishes asymptotic normality of estimators under privacy noise.

Demonstrates consistency of parameter estimators as network size grows.

Validates theoretical results with simulations and real data.

Abstract

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, 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 asymptotic results.